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Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js 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文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 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",[1800,1801,1802],"strong",{},"2026 年 8 月 1 日"," 的一手来源定向检索，不是系统综述；代码只做机制模拟。",[1805,1806,1807],"h2",{"id":1807},"学习目标",[1793,1809,1810],{},"完成本章后，你应能够：",[1812,1813,1814,1818,1821,1824,1827,1830,1833],"ol",{},[1815,1816,1817],"li",{},"用校准残差构造 split conformal 预测区间；",[1815,1819,1820],{},"准确解释“边际覆盖”而不是误写为“每个个体都有 90% 概率”；",[1815,1822,1823],{},"说明交换性、模型对称性和分布漂移如何影响覆盖保证；",[1815,1825,1826],{},"解释加权保形方法为何能缓解某些漂移、又为何不能应对任意变化；",[1815,1828,1829],{},"说明挑选重点对象后，边际覆盖为何不再等于选择条件覆盖；",[1815,1831,1832],{},"区分固定样本 p 值、随时有效 p 值、e-value 与置信序列；",[1815,1834,1835],{},"用 Ville 不等式说明为什么检验鞅允许可选停止。",[1805,1837,1839],{"id":1838},"案例一给任意预测器加上有限样本预测区间","案例一：给任意预测器加上有限样本预测区间",[1841,1842,1844],"h3",{"id":1843},"_1-问题设定","1. 问题设定",[1793,1846,1847],{},"我们有训练数据、校准数据和一个新样本：",[1849,1850,1853],"span",{"className":1851},[1852],"katex-display",[1849,1854,1857,1970],{"className":1855},[1856],"katex",[1849,1858,1861],{"className":1859},[1860],"katex-mathml",[1862,1863,1866],"math",{"xmlns":1864,"display":1865},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1867,1868,1869,1965],"semantics",{},[1870,1871,1872,1877,1888,1892,1899,1902,1904,1907,1909,1911,1918,1920,1926,1928,1930,1932,1945,1947,1959,1961],"mrow",{},[1873,1874,1876],"mo",{"stretchy":1875},"false","(",[1878,1879,1880,1884],"msub",{},[1881,1882,1883],"mi",{},"X",[1885,1886,1887],"mn",{},"1",[1873,1889,1891],{"separator":1890},"true",",",[1878,1893,1894,1897],{},[1881,1895,1896],{},"Y",[1885,1898,1887],{},[1873,1900,1901],{"stretchy":1875},")",[1873,1903,1891],{"separator":1890},[1873,1905,1906],{},"…",[1873,1908,1891],{"separator":1890},[1873,1910,1876],{"stretchy":1875},[1878,1912,1913,1915],{},[1881,1914,1883],{},[1881,1916,1917],{},"n",[1873,1919,1891],{"separator":1890},[1878,1921,1922,1924],{},[1881,1923,1896],{},[1881,1925,1917],{},[1873,1927,1901],{"stretchy":1875},[1873,1929,1891],{"separator":1890},[1873,1931,1876],{"stretchy":1875},[1878,1933,1934,1936],{},[1881,1935,1883],{},[1870,1937,1938,1940,1943],{},[1881,1939,1917],{},[1873,1941,1942],{},"+",[1885,1944,1887],{},[1873,1946,1891],{"separator":1890},[1878,1948,1949,1951],{},[1881,1950,1896],{},[1870,1952,1953,1955,1957],{},[1881,1954,1917],{},[1873,1956,1942],{},[1885,1958,1887],{},[1873,1960,1901],{"stretchy":1875},[1881,1962,1964],{"mathvariant":1963},"normal",".",[1966,1967,1969],"annotation",{"encoding":1968},"application\u002Fx-tex","(X_1,Y_1),\\ldots,(X_n,Y_n),(X_{n+1},Y_{n+1}).",[1849,1971,1974],{"className":1972,"ariaHidden":1890},[1973],"katex-html",[1849,1975,1978,1983,1987,2046,2050,2055,2097,2101,2104,2107,2111,2114,2117,2120,2123,2164,2167,2170,2210,2213,2216,2219,2222,2273,2276,2279,2328,2331],{"className":1976},[1977],"base",[1849,1979],{"className":1980,"style":1982},[1981],"strut","height:1em;vertical-align:-0.25em;",[1849,1984,1876],{"className":1985},[1986],"mopen",[1849,1988,1991,1996],{"className":1989},[1990],"mord",[1849,1992,1883],{"className":1993,"style":1995},[1990,1994],"mathnormal","margin-right:0.0785em;",[1849,1997,2000],{"className":1998},[1999],"msupsub",[1849,2001,2005,2037],{"className":2002},[2003,2004],"vlist-t","vlist-t2",[1849,2006,2009,2032],{"className":2007},[2008],"vlist-r",[1849,2010,2014],{"className":2011,"style":2013},[2012],"vlist","height:0.3011em;",[1849,2015,2017,2022],{"style":2016},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[1849,2018],{"className":2019,"style":2021},[2020],"pstrut","height:2.7em;",[1849,2023,2029],{"className":2024},[2025,2026,2027,2028],"sizing","reset-size6","size3","mtight",[1849,2030,1887],{"className":2031},[1990,2028],[1849,2033,2036],{"className":2034},[2035],"vlist-s","​",[1849,2038,2040],{"className":2039},[2008],[1849,2041,2044],{"className":2042,"style":2043},[2012],"height:0.15em;",[1849,2045],{},[1849,2047,1891],{"className":2048},[2049],"mpunct",[1849,2051],{"className":2052,"style":2054},[2053],"mspace","margin-right:0.1667em;",[1849,2056,2058,2062],{"className":2057},[1990],[1849,2059,1896],{"className":2060,"style":2061},[1990,1994],"margin-right:0.2222em;",[1849,2063,2065],{"className":2064},[1999],[1849,2066,2068,2089],{"className":2067},[2003,2004],[1849,2069,2071,2086],{"className":2070},[2008],[1849,2072,2074],{"className":2073,"style":2013},[2012],[1849,2075,2077,2080],{"style":2076},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[1849,2078],{"className":2079,"style":2021},[2020],[1849,2081,2083],{"className":2082},[2025,2026,2027,2028],[1849,2084,1887],{"className":2085},[1990,2028],[1849,2087,2036],{"className":2088},[2035],[1849,2090,2092],{"className":2091},[2008],[1849,2093,2095],{"className":2094,"style":2043},[2012],[1849,2096],{},[1849,2098,1901],{"className":2099},[2100],"mclose",[1849,2102,1891],{"className":2103},[2049],[1849,2105],{"className":2106,"style":2054},[2053],[1849,2108,1906],{"className":2109},[2110],"minner",[1849,2112],{"className":2113,"style":2054},[2053],[1849,2115,1891],{"className":2116},[2049],[1849,2118],{"className":2119,"style":2054},[2053],[1849,2121,1876],{"className":2122},[1986],[1849,2124,2126,2129],{"className":2125},[1990],[1849,2127,1883],{"className":2128,"style":1995},[1990,1994],[1849,2130,2132],{"className":2131},[1999],[1849,2133,2135,2156],{"className":2134},[2003,2004],[1849,2136,2138,2153],{"className":2137},[2008],[1849,2139,2142],{"className":2140,"style":2141},[2012],"height:0.1514em;",[1849,2143,2144,2147],{"style":2016},[1849,2145],{"className":2146,"style":2021},[2020],[1849,2148,2150],{"className":2149},[2025,2026,2027,2028],[1849,2151,1917],{"className":2152},[1990,1994,2028],[1849,2154,2036],{"className":2155},[2035],[1849,2157,2159],{"className":2158},[2008],[1849,2160,2162],{"className":2161,"style":2043},[2012],[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",[1849,2338,2340,2364],{"className":2339},[1856],[1849,2341,2343],{"className":2342},[1860],[1862,2344,2345],{"xmlns":1864},[1867,2346,2347,2361],{},[1870,2348,2349],{},[1878,2350,2351,2353],{},[1881,2352,1896],{},[1870,2354,2355,2357,2359],{},[1881,2356,1917],{},[1873,2358,1942],{},[1885,2360,1887],{},[1966,2362,2363],{"encoding":1968},"Y_{n+1}",[1849,2365,2367],{"className":2366,"ariaHidden":1890},[1973],[1849,2368,2370,2374],{"className":2369},[1977],[1849,2371],{"className":2372,"style":2373},[1981],"height:0.8917em;vertical-align:-0.2083em;",[1849,2375,2377,2380],{"className":2376},[1990],[1849,2378,1896],{"className":2379,"style":2061},[1990,1994],[1849,2381,2383],{"className":2382},[1999],[1849,2384,2386,2415],{"className":2385},[2003,2004],[1849,2387,2389,2412],{"className":2388},[2008],[1849,2390,2392],{"className":2391,"style":2013},[2012],[1849,2393,2394,2397],{"style":2076},[1849,2395],{"className":2396,"style":2021},[2020],[1849,2398,2400],{"className":2399},[2025,2026,2027,2028],[1849,2401,2403,2406,2409],{"className":2402},[1990,2028],[1849,2404,1917],{"className":2405},[1990,1994,2028],[1849,2407,1942],{"className":2408},[2257,2028],[1849,2410,1887],{"className":2411},[1990,2028],[1849,2413,2036],{"className":2414},[2035],[1849,2416,2418],{"className":2417},[2008],[1849,2419,2421],{"className":2420,"style":2270},[2012],[1849,2422],{}," 构造预测集合 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q,\\widehat\\mu(x)+\\widehat q].",[1849,3909,3911,3938,4008,4124],{"className":3910,"ariaHidden":1890},[1973],[1849,3912,3914,3917,3920,3923,3926,3929,3932,3935],{"className":3913},[1977],[1849,3915],{"className":3916,"style":1982},[1981],[1849,3918,2438],{"className":3919,"style":2470},[1990,1994],[1849,3921,1876],{"className":3922},[1986],[1849,3924,3012],{"className":3925},[1990,1994],[1849,3927,1901],{"className":3928},[2100],[1849,3930],{"className":3931,"style":2668},[2053],[1849,3933,3123],{"className":3934},[2672],[1849,3936],{"className":3937,"style":2668},[2053],[1849,3939,3941,3944,3947,3990,3993,3996,3999,4002,4005],{"className":3940},[1977],[1849,3942],{"className":3943,"style":1982},[1981],[1849,3945,3857],{"className":3946},[1986],[1849,3948,3950],{"className":3949},[1990,3030],[1849,3951,3953,3982],{"className":3952},[2003,2004],[1849,3954,3956,3979],{"className":3955},[2008],[1849,3957,3959,3967],{"className":3958,"style":3040},[2012],[1849,3960,3961,3964],{"style":3043},[1849,3962],{"className":3963,"style":3047},[2020],[1849,3965,3004],{"className":3966},[1990,1994],[1849,3968,3970,3973],{"className":3969,"style":3055},[3054],[1849,3971],{"className":3972,"style":3047},[2020],[1849,3974,3975],{"style":3061},[3063,3976,3977],{"xmlns":3065,"width":3066,"height":3067,"viewBox":3068,"preserveAspectRatio":3069},[3071,3978],{"d":3073},[1849,3980,2036],{"className":3981},[2035],[1849,3983,3985],{"className":3984},[2008],[1849,3986,3988],{"className":3987,"style":3083},[2012],[1849,3989],{},[1849,3991,1876],{"className":3992},[1986],[1849,3994,3012],{"className":3995},[1990,1994],[1849,3997,1901],{"className":3998},[2100],[1849,4000],{"className":4001,"style":2061},[2053],[1849,4003,2591],{"className":4004},[2257],[1849,4006],{"className":4007,"style":2061},[2053],[1849,4009,4011,4014,4057,4060,4063,4106,4109,4112,4115,4118,4121],{"className":4010},[1977],[1849,4012],{"className":4013,"style":1982},[1981],[1849,4015,4017],{"className":4016},[1990,3030],[1849,4018,4020,4049],{"className":4019},[2003,2004],[1849,4021,4023,4046],{"className":4022},[2008],[1849,4024,4026,4034],{"className":4025,"style":3040},[2012],[1849,4027,4028,4031],{"style":3043},[1849,4029],{"className":4030,"style":3047},[2020],[1849,4032,3766],{"className":4033,"style":3802},[1990,1994],[1849,4035,4037,4040],{"className":4036,"style":3806},[3054],[1849,4038],{"className":4039,"style":3047},[2020],[1849,4041,4042],{"style":3061},[3063,4043,4044],{"xmlns":3065,"width":3066,"height":3067,"viewBox":3068,"preserveAspectRatio":3069},[3071,4045],{"d":3073},[1849,4047,2036],{"className":4048},[2035],[1849,4050,4052],{"className":4051},[2008],[1849,4053,4055],{"className":4054,"style":3083},[2012],[1849,4056],{},[1849,4058,1891],{"className":4059},[2049],[1849,4061],{"className":4062,"style":2054},[2053],[1849,4064,4066],{"className":4065},[1990,3030],[1849,4067,4069,4098],{"className":4068},[2003,2004],[1849,4070,4072,4095],{"className":4071},[2008],[1849,4073,4075,4083],{"className":4074,"style":3040},[2012],[1849,4076,4077,4080],{"style":3043},[1849,4078],{"className":4079,"style":3047},[2020],[1849,4081,3004],{"className":4082},[1990,1994],[1849,4084,4086,4089],{"className":4085,"style":3055},[3054],[1849,4087],{"className":4088,"style":3047},[2020],[1849,4090,4091],{"style":3061},[3063,4092,4093],{"xmlns":3065,"width":3066,"height":3067,"viewBox":3068,"preserveAspectRatio":3069},[3071,4094],{"d":3073},[1849,4096,2036],{"className":4097},[2035],[1849,4099,4101],{"className":4100},[2008],[1849,4102,4104],{"className":4103,"style":3083},[2012],[1849,4105],{},[1849,4107,1876],{"className":4108},[1986],[1849,4110,3012],{"className":4111},[1990,1994],[1849,4113,1901],{"className":4114},[2100],[1849,4116],{"className":4117,"style":2061},[2053],[1849,4119,1942],{"className":4120},[2257],[1849,4122],{"className":4123,"style":2061},[2053],[1849,4125,4127,4130,4173,4176],{"className":4126},[1977],[1849,4128],{"className":4129,"style":1982},[1981],[1849,4131,4133],{"className":4132},[1990,3030],[1849,4134,4136,4165],{"className":4135},[2003,2004],[1849,4137,4139,4162],{"className":4138},[2008],[1849,4140,4142,4150],{"className":4141,"style":3040},[2012],[1849,4143,4144,4147],{"style":3043},[1849,4145],{"className":4146,"style":3047},[2020],[1849,4148,3766],{"className":4149,"style":3802},[1990,1994],[1849,4151,4153,4156],{"className":4152,"style":3806},[3054],[1849,4154],{"className":4155,"style":3047},[2020],[1849,4157,4158],{"style":3061},[3063,4159,4160],{"xmlns":3065,"width":3066,"height":3067,"viewBox":3068,"preserveAspectRatio":3069},[3071,4161],{"d":3073},[1849,4163,2036],{"className":4164},[2035],[1849,4166,4168],{"className":4167},[2008],[1849,4169,4171],{"className":4170,"style":3083},[2012],[1849,4172],{},[1849,4174,3902],{"className":4175},[2100],[1849,4177,1964],{"className":4178},[1990],[1793,4180,4181,4182,4291],{},"有限样本修正中的 ",[1849,4183,4185,4213],{"className":4184},[1856],[1849,4186,4188],{"className":4187},[1860],[1862,4189,4190],{"xmlns":1864},[1867,4191,4192,4210],{},[1870,4193,4194,4206,4208],{},[1878,4195,4196,4198],{},[1881,4197,1917],{},[1870,4199,4200,4202,4204],{},[1881,4201,2912],{},[1881,4203,2820],{},[1881,4205,2917],{},[1873,4207,1942],{},[1885,4209,1887],{},[1966,4211,4212],{"encoding":1968},"n_{cal}+1",[1849,4214,4216,4281],{"className":4215,"ariaHidden":1890},[1973],[1849,4217,4219,4223,4272,4275,4278],{"className":4218},[1977],[1849,4220],{"className":4221,"style":4222},[1981],"height:0.7333em;vertical-align:-0.15em;",[1849,4224,4226,4229],{"className":4225},[1990],[1849,4227,1917],{"className":4228},[1990,1994],[1849,4230,4232],{"className":4231},[1999],[1849,4233,4235,4264],{"className":4234},[2003,2004],[1849,4236,4238,4261],{"className":4237},[2008],[1849,4239,4241],{"className":4240,"style":2948},[2012],[1849,4242,4243,4246],{"style":3456},[1849,4244],{"className":4245,"style":2021},[2020],[1849,4247,4249],{"className":4248},[2025,2026,2027,2028],[1849,4250,4252,4255,4258],{"className":4251},[1990,2028],[1849,4253,2912],{"className":4254},[1990,1994,2028],[1849,4256,2820],{"className":4257},[1990,1994,2028],[1849,4259,2917],{"className":4260,"style":2969},[1990,1994,2028],[1849,4262,2036],{"className":4263},[2035],[1849,4265,4267],{"className":4266},[2008],[1849,4268,4270],{"className":4269,"style":2043},[2012],[1849,4271],{},[1849,4273],{"className":4274,"style":2061},[2053],[1849,4276,1942],{"className":4277},[2257],[1849,4279],{"className":4280,"style":2061},[2053],[1849,4282,4284,4288],{"className":4283},[1977],[1849,4285],{"className":4286,"style":4287},[1981],"height:0.6444em;",[1849,4289,1887],{"className":4290},[1990]," 很重要。若只调用软件默认的线性插值分位数，可能得到略低于目标的覆盖。",[1841,4293,4295],{"id":4294},"_3-为什么它有效","3. 为什么它有效",[1793,4297,4298,4299,4405],{},"在训练模型固定以后，若校准分数与新样本分数可交换，新分数在 ",[1849,4300,4302,4329],{"className":4301},[1856],[1849,4303,4305],{"className":4304},[1860],[1862,4306,4307],{"xmlns":1864},[1867,4308,4309,4327],{},[1870,4310,4311,4323,4325],{},[1878,4312,4313,4315],{},[1881,4314,1917],{},[1870,4316,4317,4319,4321],{},[1881,4318,2912],{},[1881,4320,2820],{},[1881,4322,2917],{},[1873,4324,1942],{},[1885,4326,1887],{},[1966,4328,4212],{"encoding":1968},[1849,4330,4332,4396],{"className":4331,"ariaHidden":1890},[1973],[1849,4333,4335,4338,4387,4390,4393],{"className":4334},[1977],[1849,4336],{"className":4337,"style":4222},[1981],[1849,4339,4341,4344],{"className":4340},[1990],[1849,4342,1917],{"className":4343},[1990,1994],[1849,4345,4347],{"className":4346},[1999],[1849,4348,4350,4379],{"className":4349},[2003,2004],[1849,4351,4353,4376],{"className":4352},[2008],[1849,4354,4356],{"className":4355,"style":2948},[2012],[1849,4357,4358,4361],{"style":3456},[1849,4359],{"className":4360,"style":2021},[2020],[1849,4362,4364],{"className":4363},[2025,2026,2027,2028],[1849,4365,4367,4370,4373],{"className":4366},[1990,2028],[1849,4368,2912],{"className":4369},[1990,1994,2028],[1849,4371,2820],{"className":4372},[1990,1994,2028],[1849,4374,2917],{"className":4375,"style":2969},[1990,1994,2028],[1849,4377,2036],{"className":4378},[2035],[1849,4380,4382],{"className":4381},[2008],[1849,4383,4385],{"className":4384,"style":2043},[2012],[1849,4386],{},[1849,4388],{"className":4389,"style":2061},[2053],[1849,4391,1942],{"className":4392},[2257],[1849,4394],{"className":4395,"style":2061},[2053],[1849,4397,4399,4402],{"className":4398},[1977],[1849,4400],{"className":4401,"style":4287},[1981],[1849,4403,1887],{"className":4404},[1990]," 个分数中的秩近似均匀。选取足够高的次序统计量，就能控制新分数超过阈值的概率。",[1793,4407,4408,4409,4482,4483],{},"证明依赖的是秩与交换性，而不是 ",[1849,4410,4412,4430],{"className":4411},[1856],[1849,4413,4415],{"className":4414},[1860],[1862,4416,4417],{"xmlns":1864},[1867,4418,4419,4427],{},[1870,4420,4421],{},[3000,4422,4423,4425],{"accent":1890},[1881,4424,3004],{},[1873,4426,3007],{"stretchy":1890},[1966,4428,4429],{"encoding":1968},"\\widehat\\mu",[1849,4431,4433],{"className":4432,"ariaHidden":1890},[1973],[1849,4434,4436,4439],{"className":4435},[1977],[1849,4437],{"className":4438,"style":3781},[1981],[1849,4440,4442],{"className":4441},[1990,3030],[1849,4443,4445,4474],{"className":4444},[2003,2004],[1849,4446,4448,4471],{"className":4447},[2008],[1849,4449,4451,4459],{"className":4450,"style":3040},[2012],[1849,4452,4453,4456],{"style":3043},[1849,4454],{"className":4455,"style":3047},[2020],[1849,4457,3004],{"className":4458},[1990,1994],[1849,4460,4462,4465],{"className":4461,"style":3055},[3054],[1849,4463],{"className":4464,"style":3047},[2020],[1849,4466,4467],{"style":3061},[3063,4468,4469],{"xmlns":3065,"width":3066,"height":3067,"viewBox":3068,"preserveAspectRatio":3069},[3071,4470],{"d":3073},[1849,4472,2036],{"className":4473},[2035],[1849,4475,4477],{"className":4476},[2008],[1849,4478,4480],{"className":4479,"style":3083},[2012],[1849,4481],{}," 正确。因此模型拟合很差时仍可能覆盖，但区间会很宽。",[1800,4484,4485],{},"有效覆盖不等于高效率。",[1841,4487,4489],{"id":4488},"_4-90-覆盖的准确解释","4. “90% 覆盖”的准确解释",[1793,4491,4492],{},"保证通常是对训练、校准和新样本的重复抽样取平均：",[1849,4494,4496],{"className":4495},[1852],[1849,4497,4499,4556],{"className":4498},[1856],[1849,4500,4502],{"className":4501},[1860],[1862,4503,4504],{"xmlns":1864,"display":1865},[1867,4505,4506,4553],{},[1870,4507,4508,4510,4512,4526,4528,4530,4532,4544,4546,4548,4550],{},[1881,4509,2544],{},[1873,4511,1876],{"stretchy":1875},[1878,4513,4514,4516],{},[1881,4515,1896],{},[1870,4517,4518,4520,4523],{},[1881,4519,1917],{},[1881,4521,4522],{},"e",[1881,4524,4525],{},"w",[1873,4527,2562],{},[1881,4529,2438],{},[1873,4531,1876],{"stretchy":1875},[1878,4533,4534,4536],{},[1881,4535,1883],{},[1870,4537,4538,4540,4542],{},[1881,4539,1917],{},[1881,4541,4522],{},[1881,4543,4525],{},[1873,4545,1901],{"stretchy":1875},[1873,4547,1901],{"stretchy":1875},[1873,4549,2586],{},[1885,4551,4552],{},"0.9.",[1966,4554,4555],{"encoding":1968},"P(Y_{new}\\in C(X_{new}))\\ge 0.9.",[1849,4557,4559,4630,4704],{"className":4558,"ariaHidden":1890},[1973],[1849,4560,4562,4565,4568,4571,4621,4624,4627],{"className":4561},[1977],[1849,4563],{"className":4564,"style":1982},[1981],[1849,4566,2544],{"className":4567,"style":2612},[1990,1994],[1849,4569,1876],{"className":4570},[1986],[1849,4572,4574,4577],{"className":4573},[1990],[1849,4575,1896],{"className":4576,"style":2061},[1990,1994],[1849,4578,4580],{"className":4579},[1999],[1849,4581,4583,4613],{"className":4582},[2003,2004],[1849,4584,4586,4610],{"className":4585},[2008],[1849,4587,4589],{"className":4588,"style":2141},[2012],[1849,4590,4591,4594],{"style":2076},[1849,4592],{"className":4593,"style":2021},[2020],[1849,4595,4597],{"className":4596},[2025,2026,2027,2028],[1849,4598,4600,4603,4606],{"className":4599},[1990,2028],[1849,4601,1917],{"className":4602},[1990,1994,2028],[1849,4604,4522],{"className":4605},[1990,1994,2028],[1849,4607,4525],{"className":4608,"style":4609},[1990,1994,2028],"margin-right:0.0269em;",[1849,4611,2036],{"className":4612},[2035],[1849,4614,4616],{"className":4615},[2008],[1849,4617,4619],{"className":4618,"style":2043},[2012],[1849,4620],{},[1849,4622],{"className":4623,"style":2668},[2053],[1849,4625,2562],{"className":4626},[2672],[1849,4628],{"className":4629,"style":2668},[2053],[1849,4631,4633,4636,4639,4642,4691,4695,4698,4701],{"className":4632},[1977],[1849,4634],{"className":4635,"style":1982},[1981],[1849,4637,2438],{"className":4638,"style":2470},[1990,1994],[1849,4640,1876],{"className":4641},[1986],[1849,4643,4645,4648],{"className":4644},[1990],[1849,4646,1883],{"className":4647,"style":1995},[1990,1994],[1849,4649,4651],{"className":4650},[1999],[1849,4652,4654,4683],{"className":4653},[2003,2004],[1849,4655,4657,4680],{"className":4656},[2008],[1849,4658,4660],{"className":4659,"style":2141},[2012],[1849,4661,4662,4665],{"style":2016},[1849,4663],{"className":4664,"style":2021},[2020],[1849,4666,4668],{"className":4667},[2025,2026,2027,2028],[1849,4669,4671,4674,4677],{"className":4670},[1990,2028],[1849,4672,1917],{"className":4673},[1990,1994,2028],[1849,4675,4522],{"className":4676},[1990,1994,2028],[1849,4678,4525],{"className":4679,"style":4609},[1990,1994,2028],[1849,4681,2036],{"className":4682},[2035],[1849,4684,4686],{"className":4685},[2008],[1849,4687,4689],{"className":4688,"style":2043},[2012],[1849,4690],{},[1849,4692,4694],{"className":4693},[2100],"))",[1849,4696],{"className":4697,"style":2668},[2053],[1849,4699,2586],{"className":4700},[2672],[1849,4702],{"className":4703,"style":2668},[2053],[1849,4705,4707,4710],{"className":4706},[1977],[1849,4708],{"className":4709,"style":4287},[1981],[1849,4711,4552],{"className":4712},[1990],[1793,4714,4715],{},"它一般不保证每一个协变量值都满足：",[1849,4717,4719],{"className":4718},[1852],[1849,4720,4722,4794],{"className":4721},[1856],[1849,4723,4725],{"className":4724},[1860],[1862,4726,4727],{"xmlns":1864,"display":1865},[1867,4728,4729,4791],{},[1870,4730,4731,4733,4735,4747,4749,4751,4753,4765,4767,4769,4781,4783,4785,4787,4789],{},[1881,4732,2544],{},[1873,4734,1876],{"stretchy":1875},[1878,4736,4737,4739],{},[1881,4738,1896],{},[1870,4740,4741,4743,4745],{},[1881,4742,1917],{},[1881,4744,4522],{},[1881,4746,4525],{},[1873,4748,2562],{},[1881,4750,2438],{},[1873,4752,1876],{"stretchy":1875},[1878,4754,4755,4757],{},[1881,4756,1883],{},[1870,4758,4759,4761,4763],{},[1881,4760,1917],{},[1881,4762,4522],{},[1881,4764,4525],{},[1873,4766,1901],{"stretchy":1875},[1873,4768,3126],{},[1878,4770,4771,4773],{},[1881,4772,1883],{},[1870,4774,4775,4777,4779],{},[1881,4776,1917],{},[1881,4778,4522],{},[1881,4780,4525],{},[1873,4782,3123],{},[1881,4784,3012],{},[1873,4786,1901],{"stretchy":1875},[1873,4788,2586],{},[1885,4790,4552],{},[1966,4792,4793],{"encoding":1968},"P(Y_{new}\\in C(X_{new})\\mid X_{new}=x)\\ge 0.9.",[1849,4795,4797,4867,4940,5004,5025],{"className":4796,"ariaHidden":1890},[1973],[1849,4798,4800,4803,4806,4809,4858,4861,4864],{"className":4799},[1977],[1849,4801],{"className":4802,"style":1982},[1981],[1849,4804,2544],{"className":4805,"style":2612},[1990,1994],[1849,4807,1876],{"className":4808},[1986],[1849,4810,4812,4815],{"className":4811},[1990],[1849,4813,1896],{"className":4814,"style":2061},[1990,1994],[1849,4816,4818],{"className":4817},[1999],[1849,4819,4821,4850],{"className":4820},[2003,2004],[1849,4822,4824,4847],{"className":4823},[2008],[1849,4825,4827],{"className":4826,"style":2141},[2012],[1849,4828,4829,4832],{"style":2076},[1849,4830],{"className":4831,"style":2021},[2020],[1849,4833,4835],{"className":4834},[2025,2026,2027,2028],[1849,4836,4838,4841,4844],{"className":4837},[1990,2028],[1849,4839,1917],{"className":4840},[1990,1994,2028],[1849,4842,4522],{"className":4843},[1990,1994,2028],[1849,4845,4525],{"className":4846,"style":4609},[1990,1994,2028],[1849,4848,2036],{"className":4849},[2035],[1849,4851,4853],{"className":4852},[2008],[1849,4854,4856],{"className":4855,"style":2043},[2012],[1849,4857],{},[1849,4859],{"className":4860,"style":2668},[2053],[1849,4862,2562],{"className":4863},[2672],[1849,4865],{"className":4866,"style":2668},[2053],[1849,4868,4870,4873,4876,4879,4928,4931,4934,4937],{"className":4869},[1977],[1849,4871],{"className":4872,"style":1982},[1981],[1849,4874,2438],{"className":4875,"style":2470},[1990,1994],[1849,4877,1876],{"className":4878},[1986],[1849,4880,4882,4885],{"className":4881},[1990],[1849,4883,1883],{"className":4884,"style":1995},[1990,1994],[1849,4886,4888],{"className":4887},[1999],[1849,4889,4891,4920],{"className":4890},[2003,2004],[1849,4892,4894,4917],{"className":4893},[2008],[1849,4895,4897],{"className":4896,"style":2141},[2012],[1849,4898,4899,4902],{"style":2016},[1849,4900],{"className":4901,"style":2021},[2020],[1849,4903,4905],{"className":4904},[2025,2026,2027,2028],[1849,4906,4908,4911,4914],{"className":4907},[1990,2028],[1849,4909,1917],{"className":4910},[1990,1994,2028],[1849,4912,4522],{"className":4913},[1990,1994,2028],[1849,4915,4525],{"className":4916,"style":4609},[1990,1994,2028],[1849,4918,2036],{"className":4919},[2035],[1849,4921,4923],{"className":4922},[2008],[1849,4924,4926],{"className":4925,"style":2043},[2012],[1849,4927],{},[1849,4929,1901],{"className":4930},[2100],[1849,4932],{"className":4933,"style":2668},[2053],[1849,4935,3126],{"className":4936},[2672],[1849,4938],{"className":4939,"style":2668},[2053],[1849,4941,4943,4946,4995,4998,5001],{"className":4942},[1977],[1849,4944],{"className":4945,"style":2838},[1981],[1849,4947,4949,4952],{"className":4948},[1990],[1849,4950,1883],{"className":4951,"style":1995},[1990,1994],[1849,4953,4955],{"className":4954},[1999],[1849,4956,4958,4987],{"className":4957},[2003,2004],[1849,4959,4961,4984],{"className":4960},[2008],[1849,4962,4964],{"className":4963,"style":2141},[2012],[1849,4965,4966,4969],{"style":2016},[1849,4967],{"className":4968,"style":2021},[2020],[1849,4970,4972],{"className":4971},[2025,2026,2027,2028],[1849,4973,4975,4978,4981],{"className":4974},[1990,2028],[1849,4976,1917],{"className":4977},[1990,1994,2028],[1849,4979,4522],{"className":4980},[1990,1994,2028],[1849,4982,4525],{"className":4983,"style":4609},[1990,1994,2028],[1849,4985,2036],{"className":4986},[2035],[1849,4988,4990],{"className":4989},[2008],[1849,4991,4993],{"className":4992,"style":2043},[2012],[1849,4994],{},[1849,4996],{"className":4997,"style":2668},[2053],[1849,4999,3123],{"className":5000},[2672],[1849,5002],{"className":5003,"style":2668},[2053],[1849,5005,5007,5010,5013,5016,5019,5022],{"className":5006},[1977],[1849,5008],{"className":5009,"style":1982},[1981],[1849,5011,3012],{"className":5012},[1990,1994],[1849,5014,1901],{"className":5015},[2100],[1849,5017],{"className":5018,"style":2668},[2053],[1849,5020,2586],{"className":5021},[2672],[1849,5023],{"className":5024,"style":2668},[2053],[1849,5026,5028,5031],{"className":5027},[1977],[1849,5029],{"className":5030,"style":4287},[1981],[1849,5032,4552],{"className":5033},[1990],[1793,5035,5036],{},"某些稀少亚组可能覆盖不足，另一些亚组覆盖过多。把边际保证写成“这个患者有 90% 概率落入区间”会隐藏模型、数据生成和重复抽样含义。",[1805,5038,5040],{"id":5039},"案例二部署后数据漂移交换性不再成立","案例二：部署后数据漂移，交换性不再成立",[1841,5042,5044],{"id":5043},"_1-现实中的破坏方式","1. 现实中的破坏方式",[1793,5046,5047],{},"Barber、Candès、Ramdas 与 Tibshirani（2023）研究超越交换性的保形预测。部署场景常见：",[5049,5050,5051,5054,5057,5060],"ul",{},[1815,5052,5053],{},"时间趋势使近期数据比早期数据更相关；",[1815,5055,5056],{},"传感器、医院或地区改变了协变量分布；",[1815,5058,5059],{},"训练算法对最近观测加权，因而不再对数据顺序对称；",[1815,5061,5062],{},"相邻时间点相关，不能任意置换。",[1793,5064,5065],{},"此时，传统“新分数在所有分数中的秩均匀”论证不再直接成立。",[1841,5067,5069],{"id":5068},"_2-加权分位数的直觉","2. 加权分位数的直觉",[1793,5071,5072,5073,5144],{},"若研究者能用权重 ",[1849,5074,5076,5094],{"className":5075},[1856],[1849,5077,5079],{"className":5078},[1860],[1862,5080,5081],{"xmlns":1864},[1867,5082,5083,5091],{},[1870,5084,5085],{},[1878,5086,5087,5089],{},[1881,5088,4525],{},[1881,5090,2823],{},[1966,5092,5093],{"encoding":1968},"w_i",[1849,5095,5097],{"className":5096,"ariaHidden":1890},[1973],[1849,5098,5100,5103],{"className":5099},[1977],[1849,5101],{"className":5102,"style":3435},[1981],[1849,5104,5106,5109],{"className":5105},[1990],[1849,5107,4525],{"className":5108,"style":4609},[1990,1994],[1849,5110,5112],{"className":5111},[1999],[1849,5113,5115,5136],{"className":5114},[2003,2004],[1849,5116,5118,5133],{"className":5117},[2008],[1849,5119,5121],{"className":5120,"style":2857},[2012],[1849,5122,5124,5127],{"style":5123},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1849,5125],{"className":5126,"style":2021},[2020],[1849,5128,5130],{"className":5129},[2025,2026,2027,2028],[1849,5131,2823],{"className":5132},[1990,1994,2028],[1849,5134,2036],{"className":5135},[2035],[1849,5137,5139],{"className":5138},[2008],[1849,5140,5142],{"className":5141,"style":2043},[2012],[1849,5143],{}," 表示校准观测与目标新样本的相关程度，可以使用加权经验分布：",[1849,5146,5148],{"className":5147},[1852],[1849,5149,5151,5252],{"className":5150},[1856],[1849,5152,5154],{"className":5153},[1860],[1862,5155,5156],{"xmlns":1864,"display":1865},[1867,5157,5158,5249],{},[1870,5159,5160,5171,5173,5176,5178,5180,5247],{},[1878,5161,5162,5169],{},[3000,5163,5164,5167],{"accent":1890},[1881,5165,5166],{},"F",[1873,5168,3007],{"stretchy":1890},[1881,5170,4525],{},[1873,5172,1876],{"stretchy":1875},[1881,5174,5175],{},"s",[1873,5177,1901],{"stretchy":1875},[1873,5179,3123],{},[5181,5182,5183,5225],"mfrac",{},[1870,5184,5185,5201,5207,5210,5212,5218,5221,5223],{},[5186,5187,5188,5191,5199],"munderover",{},[1873,5189,5190],{},"∑",[1870,5192,5193,5195,5197],{},[1881,5194,2823],{},[1873,5196,3123],{},[1885,5198,1887],{},[1881,5200,1917],{},[1878,5202,5203,5205],{},[1881,5204,4525],{},[1881,5206,2823],{},[1885,5208,1887],{"mathvariant":5209},"bold",[1873,5211,1876],{"stretchy":1875},[1878,5213,5214,5216],{},[1881,5215,3118],{},[1881,5217,2823],{},[1873,5219,5220],{},"≤",[1881,5222,5175],{},[1873,5224,1901],{"stretchy":1875},[1870,5226,5227,5241],{},[5186,5228,5229,5231,5239],{},[1873,5230,5190],{},[1870,5232,5233,5235,5237],{},[1881,5234,2823],{},[1873,5236,3123],{},[1885,5238,1887],{},[1881,5240,1917],{},[1878,5242,5243,5245],{},[1881,5244,4525],{},[1881,5246,2823],{},[1881,5248,1964],{"mathvariant":1963},[1966,5250,5251],{"encoding":1968},"\\widehat F_w(s)\n=\\frac{\\sum_{i=1}^{n}w_i\\mathbf 1(S_i\\le s)}\n{\\sum_{i=1}^{n}w_i}.",[1849,5253,5255,5352],{"className":5254,"ariaHidden":1890},[1973],[1849,5256,5258,5262,5334,5337,5340,5343,5346,5349],{"className":5257},[1977],[1849,5259],{"className":5260,"style":5261},[1981],"height:1.1733em;vertical-align:-0.25em;",[1849,5263,5265,5299],{"className":5264},[1990],[1849,5266,5268],{"className":5267},[1990,3030],[1849,5269,5271],{"className":5270},[2003],[1849,5272,5274],{"className":5273},[2008],[1849,5275,5278,5286],{"className":5276,"style":5277},[2012],"height:0.9233em;",[1849,5279,5280,5283],{"style":3043},[1849,5281],{"className":5282,"style":3047},[2020],[1849,5284,5166],{"className":5285,"style":2612},[1990,1994],[1849,5287,5290,5293],{"className":5288,"style":5289},[3054],"width:calc(100% - 0.1667em);margin-left:0.1667em;top:-3.6833em;",[1849,5291],{"className":5292,"style":3047},[2020],[1849,5294,5295],{"style":3061},[3063,5296,5297],{"xmlns":3065,"width":3066,"height":3067,"viewBox":3068,"preserveAspectRatio":3069},[3071,5298],{"d":3073},[1849,5300,5302],{"className":5301},[1999],[1849,5303,5305,5326],{"className":5304},[2003,2004],[1849,5306,5308,5323],{"className":5307},[2008],[1849,5309,5311],{"className":5310,"style":2141},[2012],[1849,5312,5314,5317],{"style":5313},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1849,5315],{"className":5316,"style":2021},[2020],[1849,5318,5320],{"className":5319},[2025,2026,2027,2028],[1849,5321,4525],{"className":5322,"style":4609},[1990,1994,2028],[1849,5324,2036],{"className":5325},[2035],[1849,5327,5329],{"className":5328},[2008],[1849,5330,5332],{"className":5331,"style":2043},[2012],[1849,5333],{},[1849,5335,1876],{"className":5336},[1986],[1849,5338,5175],{"className":5339},[1990,1994],[1849,5341,1901],{"className":5342},[2100],[1849,5344],{"className":5345,"style":2668},[2053],[1849,5347,3123],{"className":5348},[2672],[1849,5350],{"className":5351,"style":2668},[2053],[1849,5353,5355,5359,5705],{"className":5354},[1977],[1849,5356],{"className":5357,"style":5358},[1981],"height:2.488em;vertical-align:-0.994em;",[1849,5360,5362,5366,5702],{"className":5361},[1990],[1849,5363],{"className":5364},[1986,5365],"nulldelimiter",[1849,5367,5369],{"className":5368},[5181],[1849,5370,5372,5693],{"className":5371},[2003,2004],[1849,5373,5375,5690],{"className":5374},[2008],[1849,5376,5379,5502,5513],{"className":5377,"style":5378},[2012],"height:1.494em;",[1849,5380,5382,5385],{"style":5381},"top:-2.3057em;",[1849,5383],{"className":5384,"style":3047},[2020],[1849,5386,5388,5459,5462],{"className":5387},[1990],[1849,5389,5392,5398],{"className":5390},[5391],"mop",[1849,5393,5190],{"className":5394,"style":5397},[5391,5395,5396],"op-symbol","small-op","position:relative;top:0em;",[1849,5399,5401],{"className":5400},[1999],[1849,5402,5404,5450],{"className":5403},[2003,2004],[1849,5405,5407,5447],{"className":5406},[2008],[1849,5408,5411,5432],{"className":5409,"style":5410},[2012],"height:0.8043em;",[1849,5412,5414,5417],{"style":5413},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1849,5415],{"className":5416,"style":2021},[2020],[1849,5418,5420],{"className":5419},[2025,2026,2027,2028],[1849,5421,5423,5426,5429],{"className":5422},[1990,2028],[1849,5424,2823],{"className":5425},[1990,1994,2028],[1849,5427,3123],{"className":5428},[2672,2028],[1849,5430,1887],{"className":5431},[1990,2028],[1849,5433,5435,5438],{"style":5434},"top:-3.2029em;margin-right:0.05em;",[1849,5436],{"className":5437,"style":2021},[2020],[1849,5439,5441],{"className":5440},[2025,2026,2027,2028],[1849,5442,5444],{"className":5443},[1990,2028],[1849,5445,1917],{"className":5446},[1990,1994,2028],[1849,5448,2036],{"className":5449},[2035],[1849,5451,5453],{"className":5452},[2008],[1849,5454,5457],{"className":5455,"style":5456},[2012],"height:0.2997em;",[1849,5458],{},[1849,5460],{"className":5461,"style":2054},[2053],[1849,5463,5465,5468],{"className":5464},[1990],[1849,5466,4525],{"className":5467,"style":4609},[1990,1994],[1849,5469,5471],{"className":5470},[1999],[1849,5472,5474,5494],{"className":5473},[2003,2004],[1849,5475,5477,5491],{"className":5476},[2008],[1849,5478,5480],{"className":5479,"style":2857},[2012],[1849,5481,5482,5485],{"style":5123},[1849,5483],{"className":5484,"style":2021},[2020],[1849,5486,5488],{"className":5487},[2025,2026,2027,2028],[1849,5489,2823],{"className":5490},[1990,1994,2028],[1849,5492,2036],{"className":5493},[2035],[1849,5495,5497],{"className":5496},[2008],[1849,5498,5500],{"className":5499,"style":2043},[2012],[1849,5501],{},[1849,5503,5505,5508],{"style":5504},"top:-3.23em;",[1849,5506],{"className":5507,"style":3047},[2020],[1849,5509],{"className":5510,"style":5512},[5511],"frac-line","border-bottom-width:0.04em;",[1849,5514,5516,5519],{"style":5515},"top:-3.6897em;",[1849,5517],{"className":5518,"style":3047},[2020],[1849,5520,5522,5585,5588,5628,5632,5635,5675,5678,5681,5684,5687],{"className":5521},[1990],[1849,5523,5525,5528],{"className":5524},[5391],[1849,5526,5190],{"className":5527,"style":5397},[5391,5395,5396],[1849,5529,5531],{"className":5530},[1999],[1849,5532,5534,5577],{"className":5533},[2003,2004],[1849,5535,5537,5574],{"className":5536},[2008],[1849,5538,5540,5560],{"className":5539,"style":5410},[2012],[1849,5541,5542,5545],{"style":5413},[1849,5543],{"className":5544,"style":2021},[2020],[1849,5546,5548],{"className":5547},[2025,2026,2027,2028],[1849,5549,5551,5554,5557],{"className":5550},[1990,2028],[1849,5552,2823],{"className":5553},[1990,1994,2028],[1849,5555,3123],{"className":5556},[2672,2028],[1849,5558,1887],{"className":5559},[1990,2028],[1849,5561,5562,5565],{"style":5434},[1849,5563],{"className":5564,"style":2021},[2020],[1849,5566,5568],{"className":5567},[2025,2026,2027,2028],[1849,5569,5571],{"className":5570},[1990,2028],[1849,5572,1917],{"className":5573},[1990,1994,2028],[1849,5575,2036],{"className":5576},[2035],[1849,5578,5580],{"className":5579},[2008],[1849,5581,5583],{"className":5582,"style":5456},[2012],[1849,5584],{},[1849,5586],{"className":5587,"style":2054},[2053],[1849,5589,5591,5594],{"className":5590},[1990],[1849,5592,4525],{"className":5593,"style":4609},[1990,1994],[1849,5595,5597],{"className":5596},[1999],[1849,5598,5600,5620],{"className":5599},[2003,2004],[1849,5601,5603,5617],{"className":5602},[2008],[1849,5604,5606],{"className":5605,"style":2857},[2012],[1849,5607,5608,5611],{"style":5123},[1849,5609],{"className":5610,"style":2021},[2020],[1849,5612,5614],{"className":5613},[2025,2026,2027,2028],[1849,5615,2823],{"className":5616},[1990,1994,2028],[1849,5618,2036],{"className":5619},[2035],[1849,5621,5623],{"className":5622},[2008],[1849,5624,5626],{"className":5625,"style":2043},[2012],[1849,5627],{},[1849,5629,1887],{"className":5630},[1990,5631],"mathbf",[1849,5633,1876],{"className":5634},[1986],[1849,5636,5638,5641],{"className":5637},[1990],[1849,5639,3118],{"className":5640,"style":3174},[1990,1994],[1849,5642,5644],{"className":5643},[1999],[1849,5645,5647,5667],{"className":5646},[2003,2004],[1849,5648,5650,5664],{"className":5649},[2008],[1849,5651,5653],{"className":5652,"style":2857},[2012],[1849,5654,5655,5658],{"style":3189},[1849,5656],{"className":5657,"style":2021},[2020],[1849,5659,5661],{"className":5660},[2025,2026,2027,2028],[1849,5662,2823],{"className":5663},[1990,1994,2028],[1849,5665,2036],{"className":5666},[2035],[1849,5668,5670],{"className":5669},[2008],[1849,5671,5673],{"className":5672,"style":2043},[2012],[1849,5674],{},[1849,5676],{"className":5677,"style":2668},[2053],[1849,5679,5220],{"className":5680},[2672],[1849,5682],{"className":5683,"style":2668},[2053],[1849,5685,5175],{"className":5686},[1990,1994],[1849,5688,1901],{"className":5689},[2100],[1849,5691,2036],{"className":5692},[2035],[1849,5694,5696],{"className":5695},[2008],[1849,5697,5700],{"className":5698,"style":5699},[2012],"height:0.994em;",[1849,5701],{},[1849,5703],{"className":5704},[2100,5365],[1849,5706,1964],{"className":5707},[1990],[1793,5709,5710,5711,5815],{},"近期或更接近目标分布的观测获得较高权重，再从 ",[1849,5712,5714,5736],{"className":5713},[1856],[1849,5715,5717],{"className":5716},[1860],[1862,5718,5719],{"xmlns":1864},[1867,5720,5721,5733],{},[1870,5722,5723],{},[1878,5724,5725,5731],{},[3000,5726,5727,5729],{"accent":1890},[1881,5728,5166],{},[1873,5730,3007],{"stretchy":1890},[1881,5732,4525],{},[1966,5734,5735],{"encoding":1968},"\\widehat F_w",[1849,5737,5739],{"className":5738,"ariaHidden":1890},[1973],[1849,5740,5742,5746],{"className":5741},[1977],[1849,5743],{"className":5744,"style":5745},[1981],"height:1.0733em;vertical-align:-0.15em;",[1849,5747,5749,5781],{"className":5748},[1990],[1849,5750,5752],{"className":5751},[1990,3030],[1849,5753,5755],{"className":5754},[2003],[1849,5756,5758],{"className":5757},[2008],[1849,5759,5761,5769],{"className":5760,"style":5277},[2012],[1849,5762,5763,5766],{"style":3043},[1849,5764],{"className":5765,"style":3047},[2020],[1849,5767,5166],{"className":5768,"style":2612},[1990,1994],[1849,5770,5772,5775],{"className":5771,"style":5289},[3054],[1849,5773],{"className":5774,"style":3047},[2020],[1849,5776,5777],{"style":3061},[3063,5778,5779],{"xmlns":3065,"width":3066,"height":3067,"viewBox":3068,"preserveAspectRatio":3069},[3071,5780],{"d":3073},[1849,5782,5784],{"className":5783},[1999],[1849,5785,5787,5807],{"className":5786},[2003,2004],[1849,5788,5790,5804],{"className":5789},[2008],[1849,5791,5793],{"className":5792,"style":2141},[2012],[1849,5794,5795,5798],{"style":5313},[1849,5796],{"className":5797,"style":2021},[2020],[1849,5799,5801],{"className":5800},[2025,2026,2027,2028],[1849,5802,4525],{"className":5803,"style":4609},[1990,1994,2028],[1849,5805,2036],{"className":5806},[2035],[1849,5808,5810],{"className":5809},[2008],[1849,5811,5813],{"className":5812,"style":2043},[2012],[1849,5814],{}," 取分位数。论文同时设计随机化技术，处理拟合算法不对称的问题，并给出对分布漂移的稳健性界。",[1841,5817,5819],{"id":5818},"_3-不能过度承诺什么","3. 不能过度承诺什么",[1793,5821,5822],{},"权重必须与漂移结构有关。若未来出现校准样本从未覆盖的新机制、结果定义改变或标签测量失真，没有一个机械加权分位数可以凭空恢复保证。越偏离交换性，结论越依赖对漂移的建模与界定。",[1793,5824,5825],{},"学生应把“不确定性量化”分为两层：",[1812,5827,5828,5833],{},[1815,5829,5830,3095],{},[1800,5831,5832],{},"给定假设下的数学保证",[1815,5834,5835,5838],{},[1800,5836,5837],{},"假设在部署环境中是否可信的监测证据","。",[1841,5840,5842],{"id":5841},"_4-2026-年延伸目标数据少时能否借用其他来源","4. 2026 年延伸：目标数据少时能否借用其他来源",[1793,5844,5845,5846,5850],{},"Zhang 等（2026）在 ",[5847,5848,5849],"em",{},"Journal of Machine Learning Research"," 研究 transfer conformal：目标人群校准数据很少时，能否借用相关来源数据缩短区间。关键不是把所有来源直接合并，而是识别哪些来源对目标条件分布有信息，并允许来源与目标不交换。论文用条件 Kullback–Leibler 散度选择相关来源，并分析覆盖与区间宽度的非渐近性质。",[1793,5852,5853],{},"这类方法把“更多数据”拆成两个问题：",[1812,5855,5856,5859],{},[1815,5857,5858],{},"来源数据能否提高精度？",[1815,5860,5861],{},"来源与目标差异是否仍在方法保证覆盖的范围内？",[1793,5863,5864],{},"若医院改变了结果定义、传感器出现系统偏差，或目标人群包含来源中不存在的亚组，迁移算法不能凭数据量恢复可比性。",[1805,5866,5868],{"id":5867},"案例三选择了重点对象以后边际覆盖还够吗","案例三：选择了重点对象以后，边际覆盖还够吗",[1793,5870,5871],{},"标准 conformal 保证针对一个随机测试点的边际覆盖。实践中却常先看风险分数，再挑出最高风险患者、最有希望药物或最异常账户。被选中的对象不是随机测试点；它们集中在模型最不稳定或噪声最大的区域时，原边际覆盖可能明显不足。",[1793,5873,5874,5875,5878,5879,5909],{},"Jin 与 Ren（2025）在 ",[5847,5876,5877],{},"Journal of the Royal Statistical Society: Series B"," 提出选择条件覆盖框架：给定对象被某个程序选中后，预测集合仍具有有限样本精确覆盖。框架允许多种对校准单位置换不变的选择规则，包括 top-",[1849,5880,5882,5896],{"className":5881},[1856],[1849,5883,5885],{"className":5884},[1860],[1862,5886,5887],{"xmlns":1864},[1867,5888,5889,5894],{},[1870,5890,5891],{},[1881,5892,5893],{},"K",[1966,5895,5893],{"encoding":1968},[1849,5897,5899],{"className":5898,"ariaHidden":1890},[1973],[1849,5900,5902,5906],{"className":5901},[1977],[1849,5903],{"className":5904,"style":5905},[1981],"height:0.6833em;",[1849,5907,5893],{"className":5908,"style":2470},[1990,1994],"、优化型选择和按初步 conformal 集合选择。",[1793,5911,5912],{},"教学上要区分：",[5914,5915,5916,5932],"table",{},[5917,5918,5919],"thead",{},[5920,5921,5922,5926,5929],"tr",{},[5923,5924,5925],"th",{},"保证",[5923,5927,5928],{},"重复抽样对象",[5923,5930,5931],{},"适合问题",[5933,5934,5935,5947,6010,6050],"tbody",{},[5920,5936,5937,5941,5944],{},[5938,5939,5940],"td",{},"边际覆盖",[5938,5942,5943],{},"随机抽取一个新单位",[5938,5945,5946],{},"普通总体预测",[5920,5948,5949,6004,6007],{},[5938,5950,5951,5952,6003],{},"条件于 ",[1849,5953,5955,5973],{"className":5954},[1856],[1849,5956,5958],{"className":5957},[1860],[1862,5959,5960],{"xmlns":1864},[1867,5961,5962,5970],{},[1870,5963,5964,5966,5968],{},[1881,5965,1883],{},[1873,5967,3123],{},[1881,5969,3012],{},[1966,5971,5972],{"encoding":1968},"X=x",[1849,5974,5976,5994],{"className":5975,"ariaHidden":1890},[1973],[1849,5977,5979,5982,5985,5988,5991],{"className":5978},[1977],[1849,5980],{"className":5981,"style":5905},[1981],[1849,5983,1883],{"className":5984,"style":1995},[1990,1994],[1849,5986],{"className":5987,"style":2668},[2053],[1849,5989,3123],{"className":5990},[2672],[1849,5992],{"className":5993,"style":2668},[2053],[1849,5995,5997,6000],{"className":5996},[1977],[1849,5998],{"className":5999,"style":2775},[1981],[1849,6001,3012],{"className":6002},[1990,1994]," 的覆盖",[5938,6005,6006],{},"固定协变量位置",[5938,6008,6009],{},"每类人都要校准",[5920,6011,6012,6015,6018],{},[5938,6013,6014],{},"选择条件覆盖",[5938,6016,6017],{},"给定单位被规则选中",[5938,6019,6020,6021,6049],{},"只处理高风险\u002Ftop-",[1849,6022,6024,6037],{"className":6023},[1856],[1849,6025,6027],{"className":6026},[1860],[1862,6028,6029],{"xmlns":1864},[1867,6030,6031,6035],{},[1870,6032,6033],{},[1881,6034,5893],{},[1966,6036,5893],{"encoding":1968},[1849,6038,6040],{"className":6039,"ariaHidden":1890},[1973],[1849,6041,6043,6046],{"className":6042},[1977],[1849,6044],{"className":6045,"style":5905},[1981],[1849,6047,5893],{"className":6048,"style":2470},[1990,1994]," 对象",[5920,6051,6052,6055,6058],{},[5938,6053,6054],{},"false coverage rate",[5938,6056,6057],{},"多个被选集合中的平均错误比例",[5938,6059,6060],{},"批量筛选",[1793,6062,6063],{},"选择条件方法不是免费升级：区间可能变宽，且保证依赖选择规则被完整纳入推断。临时改选对象或只报告窄区间，会再次引入选择偏误。",[1805,6065,6067],{"id":6066},"案例四可以反复看数据而不破坏错误率吗","案例四：可以反复看数据而不破坏错误率吗",[1841,6069,6071],{"id":6070},"_1-固定样本检验的窥视问题","1. 固定样本检验的窥视问题",[1793,6073,6074,6075,6103,6104,6158],{},"传统检验先固定样本量 ",[1849,6076,6078,6091],{"className":6077},[1856],[1849,6079,6081],{"className":6080},[1860],[1862,6082,6083],{"xmlns":1864},[1867,6084,6085,6089],{},[1870,6086,6087],{},[1881,6088,1917],{},[1966,6090,1917],{"encoding":1968},[1849,6092,6094],{"className":6093,"ariaHidden":1890},[1973],[1849,6095,6097,6100],{"className":6096},[1977],[1849,6098],{"className":6099,"style":2775},[1981],[1849,6101,1917],{"className":6102},[1990,1994],"，再在末尾计算 p 值。如果研究者每天查看一次结果，并在第一次 ",[1849,6105,6107,6127],{"className":6106},[1856],[1849,6108,6110],{"className":6109},[1860],[1862,6111,6112],{"xmlns":1864},[1867,6113,6114,6124],{},[1870,6115,6116,6118,6121],{},[1881,6117,1793],{},[1873,6119,6120],{},"\u003C",[1885,6122,6123],{},"0.05",[1966,6125,6126],{"encoding":1968},"p\u003C0.05",[1849,6128,6130,6149],{"className":6129,"ariaHidden":1890},[1973],[1849,6131,6133,6137,6140,6143,6146],{"className":6132},[1977],[1849,6134],{"className":6135,"style":6136},[1981],"height:0.7335em;vertical-align:-0.1944em;",[1849,6138,1793],{"className":6139},[1990,1994],[1849,6141],{"className":6142,"style":2668},[2053],[1849,6144,6120],{"className":6145},[2672],[1849,6147],{"className":6148,"style":2668},[2053],[1849,6150,6152,6155],{"className":6151},[1977],[1849,6153],{"className":6154,"style":4287},[1981],[1849,6156,6123],{"className":6157},[1990]," 时停止，那么实际一类错误率可能超过 5%。原因是停止规则本身选择了看起来最极端的时点。",[1793,6160,6161],{},"Ramdas、Grünwald、Vovk 与 Shafer（2023）综述了 safe anytime-valid inference（SAVI）。核心对象包括 e-process 与置信序列，它们在任意停止时刻仍保持有效。",[1841,6163,6165],{"id":6164},"_2-从赌博财富理解-e-value","2. 从赌博财富理解 e-value",[1793,6167,6168,6169,6264],{},"设 ",[1849,6170,6172,6196],{"className":6171},[1856],[1849,6173,6175],{"className":6174},[1860],[1862,6176,6177],{"xmlns":1864},[1867,6178,6179,6193],{},[1870,6180,6181,6188,6190],{},[1878,6182,6183,6186],{},[1881,6184,6185],{},"E",[1881,6187,2814],{},[1873,6189,2586],{},[1885,6191,6192],{},"0",[1966,6194,6195],{"encoding":1968},"E_t\\ge0",[1849,6197,6199,6255],{"className":6198,"ariaHidden":1890},[1973],[1849,6200,6202,6205,6246,6249,6252],{"className":6201},[1977],[1849,6203],{"className":6204,"style":2838},[1981],[1849,6206,6208,6211],{"className":6207},[1990],[1849,6209,6185],{"className":6210,"style":3174},[1990,1994],[1849,6212,6214],{"className":6213},[1999],[1849,6215,6217,6238],{"className":6216},[2003,2004],[1849,6218,6220,6235],{"className":6219},[2008],[1849,6221,6224],{"className":6222,"style":6223},[2012],"height:0.2806em;",[1849,6225,6226,6229],{"style":3189},[1849,6227],{"className":6228,"style":2021},[2020],[1849,6230,6232],{"className":6231},[2025,2026,2027,2028],[1849,6233,2814],{"className":6234},[1990,1994,2028],[1849,6236,2036],{"className":6237},[2035],[1849,6239,6241],{"className":6240},[2008],[1849,6242,6244],{"className":6243,"style":2043},[2012],[1849,6245],{},[1849,6247],{"className":6248,"style":2668},[2053],[1849,6250,2586],{"className":6251},[2672],[1849,6253],{"className":6254,"style":2668},[2053],[1849,6256,6258,6261],{"className":6257},[1977],[1849,6259],{"className":6260,"style":4287},[1981],[1849,6262,6192],{"className":6263},[1990]," 是在原假设成立时满足",[1849,6266,6268],{"className":6267},[1852],[1849,6269,6271,6308],{"className":6270},[1856],[1849,6272,6274],{"className":6273},[1860],[1862,6275,6276],{"xmlns":1864,"display":1865},[1867,6277,6278,6305],{},[1870,6279,6280,6291,6293,6299,6301,6303],{},[1878,6281,6282,6284],{},[1881,6283,6185],{},[1878,6285,6286,6289],{},[1881,6287,6288],{},"H",[1885,6290,6192],{},[1873,6292,3857],{"stretchy":1875},[1878,6294,6295,6297],{},[1881,6296,6185],{},[1881,6298,2814],{},[1873,6300,3902],{"stretchy":1875},[1873,6302,5220],{},[1885,6304,1887],{},[1966,6306,6307],{"encoding":1968},"E_{H_0}[E_t]\\le1\n",[1849,6309,6311,6462],{"className":6310,"ariaHidden":1890},[1973],[1849,6312,6314,6318,6407,6410,6450,6453,6456,6459],{"className":6313},[1977],[1849,6315],{"className":6316,"style":6317},[1981],"height:1.0001em;vertical-align:-0.2501em;",[1849,6319,6321,6324],{"className":6320},[1990],[1849,6322,6185],{"className":6323,"style":3174},[1990,1994],[1849,6325,6327],{"className":6326},[1999],[1849,6328,6330,6398],{"className":6329},[2003,2004],[1849,6331,6333,6395],{"className":6332},[2008],[1849,6334,6337],{"className":6335,"style":6336},[2012],"height:0.3283em;",[1849,6338,6339,6342],{"style":3189},[1849,6340],{"className":6341,"style":2021},[2020],[1849,6343,6345],{"className":6344},[2025,2026,2027,2028],[1849,6346,6348],{"className":6347},[1990,2028],[1849,6349,6351,6355],{"className":6350},[1990,2028],[1849,6352,6288],{"className":6353,"style":6354},[1990,1994,2028],"margin-right:0.0813em;",[1849,6356,6358],{"className":6357},[1999],[1849,6359,6361,6386],{"className":6360},[2003,2004],[1849,6362,6364,6383],{"className":6363},[2008],[1849,6365,6368],{"className":6366,"style":6367},[2012],"height:0.3173em;",[1849,6369,6371,6375],{"style":6370},"top:-2.357em;margin-left:-0.0813em;margin-right:0.0714em;",[1849,6372],{"className":6373,"style":6374},[2020],"height:2.5em;",[1849,6376,6380],{"className":6377},[2025,6378,6379,2028],"reset-size3","size1",[1849,6381,6192],{"className":6382},[1990,2028],[1849,6384,2036],{"className":6385},[2035],[1849,6387,6389],{"className":6388},[2008],[1849,6390,6393],{"className":6391,"style":6392},[2012],"height:0.143em;",[1849,6394],{},[1849,6396,2036],{"className":6397},[2035],[1849,6399,6401],{"className":6400},[2008],[1849,6402,6405],{"className":6403,"style":6404},[2012],"height:0.2501em;",[1849,6406],{},[1849,6408,3857],{"className":6409},[1986],[1849,6411,6413,6416],{"className":6412},[1990],[1849,6414,6185],{"className":6415,"style":3174},[1990,1994],[1849,6417,6419],{"className":6418},[1999],[1849,6420,6422,6442],{"className":6421},[2003,2004],[1849,6423,6425,6439],{"className":6424},[2008],[1849,6426,6428],{"className":6427,"style":6223},[2012],[1849,6429,6430,6433],{"style":3189},[1849,6431],{"className":6432,"style":2021},[2020],[1849,6434,6436],{"className":6435},[2025,2026,2027,2028],[1849,6437,2814],{"className":6438},[1990,1994,2028],[1849,6440,2036],{"className":6441},[2035],[1849,6443,6445],{"className":6444},[2008],[1849,6446,6448],{"className":6447,"style":2043},[2012],[1849,6449],{},[1849,6451,3902],{"className":6452},[2100],[1849,6454],{"className":6455,"style":2668},[2053],[1849,6457,5220],{"className":6458},[2672],[1849,6460],{"className":6461,"style":2668},[2053],[1849,6463,6465,6468],{"className":6464},[1977],[1849,6466],{"className":6467,"style":4287},[1981],[1849,6469,1887],{"className":6470},[1990],[1793,6472,6473,6474,6544,6545,6616,6617,6700,6701,6793],{},"的 e-value。较大的 ",[1849,6475,6477,6495],{"className":6476},[1856],[1849,6478,6480],{"className":6479},[1860],[1862,6481,6482],{"xmlns":1864},[1867,6483,6484,6492],{},[1870,6485,6486],{},[1878,6487,6488,6490],{},[1881,6489,6185],{},[1881,6491,2814],{},[1966,6493,6494],{"encoding":1968},"E_t",[1849,6496,6498],{"className":6497,"ariaHidden":1890},[1973],[1849,6499,6501,6504],{"className":6500},[1977],[1849,6502],{"className":6503,"style":2838},[1981],[1849,6505,6507,6510],{"className":6506},[1990],[1849,6508,6185],{"className":6509,"style":3174},[1990,1994],[1849,6511,6513],{"className":6512},[1999],[1849,6514,6516,6536],{"className":6515},[2003,2004],[1849,6517,6519,6533],{"className":6518},[2008],[1849,6520,6522],{"className":6521,"style":6223},[2012],[1849,6523,6524,6527],{"style":3189},[1849,6525],{"className":6526,"style":2021},[2020],[1849,6528,6530],{"className":6529},[2025,2026,2027,2028],[1849,6531,2814],{"className":6532},[1990,1994,2028],[1849,6534,2036],{"className":6535},[2035],[1849,6537,6539],{"className":6538},[2008],[1849,6540,6542],{"className":6541,"style":2043},[2012],[1849,6543],{}," 是反对 ",[1849,6546,6548,6566],{"className":6547},[1856],[1849,6549,6551],{"className":6550},[1860],[1862,6552,6553],{"xmlns":1864},[1867,6554,6555,6563],{},[1870,6556,6557],{},[1878,6558,6559,6561],{},[1881,6560,6288],{},[1885,6562,6192],{},[1966,6564,6565],{"encoding":1968},"H_0",[1849,6567,6569],{"className":6568,"ariaHidden":1890},[1973],[1849,6570,6572,6575],{"className":6571},[1977],[1849,6573],{"className":6574,"style":2838},[1981],[1849,6576,6578,6581],{"className":6577},[1990],[1849,6579,6288],{"className":6580,"style":6354},[1990,1994],[1849,6582,6584],{"className":6583},[1999],[1849,6585,6587,6608],{"className":6586},[2003,2004],[1849,6588,6590,6605],{"className":6589},[2008],[1849,6591,6593],{"className":6592,"style":2013},[2012],[1849,6594,6596,6599],{"style":6595},"top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;",[1849,6597],{"className":6598,"style":2021},[2020],[1849,6600,6602],{"className":6601},[2025,2026,2027,2028],[1849,6603,6192],{"className":6604},[1990,2028],[1849,6606,2036],{"className":6607},[2035],[1849,6609,6611],{"className":6610},[2008],[1849,6612,6614],{"className":6613,"style":2043},[2012],[1849,6615],{}," 的证据。若 ",[1849,6618,6620,6643],{"className":6619},[1856],[1849,6621,6623],{"className":6622},[1860],[1862,6624,6625],{"xmlns":1864},[1867,6626,6627,6640],{},[1870,6628,6629,6631,6638],{},[1873,6630,1876],{"stretchy":1875},[1878,6632,6633,6636],{},[1881,6634,6635],{},"M",[1881,6637,2814],{},[1873,6639,1901],{"stretchy":1875},[1966,6641,6642],{"encoding":1968},"(M_t)",[1849,6644,6646],{"className":6645,"ariaHidden":1890},[1973],[1849,6647,6649,6652,6655,6697],{"className":6648},[1977],[1849,6650],{"className":6651,"style":1982},[1981],[1849,6653,1876],{"className":6654},[1986],[1849,6656,6658,6662],{"className":6657},[1990],[1849,6659,6635],{"className":6660,"style":6661},[1990,1994],"margin-right:0.109em;",[1849,6663,6665],{"className":6664},[1999],[1849,6666,6668,6689],{"className":6667},[2003,2004],[1849,6669,6671,6686],{"className":6670},[2008],[1849,6672,6674],{"className":6673,"style":6223},[2012],[1849,6675,6677,6680],{"style":6676},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[1849,6678],{"className":6679,"style":2021},[2020],[1849,6681,6683],{"className":6682},[2025,2026,2027,2028],[1849,6684,2814],{"className":6685},[1990,1994,2028],[1849,6687,2036],{"className":6688},[2035],[1849,6690,6692],{"className":6691},[2008],[1849,6693,6695],{"className":6694,"style":2043},[2012],[1849,6696],{},[1849,6698,1901],{"className":6699},[2100]," 是从 ",[1849,6702,6704,6726],{"className":6703},[1856],[1849,6705,6707],{"className":6706},[1860],[1862,6708,6709],{"xmlns":1864},[1867,6710,6711,6723],{},[1870,6712,6713,6719,6721],{},[1878,6714,6715,6717],{},[1881,6716,6635],{},[1885,6718,6192],{},[1873,6720,3123],{},[1885,6722,1887],{},[1966,6724,6725],{"encoding":1968},"M_0=1",[1849,6727,6729,6784],{"className":6728,"ariaHidden":1890},[1973],[1849,6730,6732,6735,6775,6778,6781],{"className":6731},[1977],[1849,6733],{"className":6734,"style":2838},[1981],[1849,6736,6738,6741],{"className":6737},[1990],[1849,6739,6635],{"className":6740,"style":6661},[1990,1994],[1849,6742,6744],{"className":6743},[1999],[1849,6745,6747,6767],{"className":6746},[2003,2004],[1849,6748,6750,6764],{"className":6749},[2008],[1849,6751,6753],{"className":6752,"style":2013},[2012],[1849,6754,6755,6758],{"style":6676},[1849,6756],{"className":6757,"style":2021},[2020],[1849,6759,6761],{"className":6760},[2025,2026,2027,2028],[1849,6762,6192],{"className":6763},[1990,2028],[1849,6765,2036],{"className":6766},[2035],[1849,6768,6770],{"className":6769},[2008],[1849,6771,6773],{"className":6772,"style":2043},[2012],[1849,6774],{},[1849,6776],{"className":6777,"style":2668},[2053],[1849,6779,3123],{"className":6780},[2672],[1849,6782],{"className":6783,"style":2668},[2053],[1849,6785,6787,6790],{"className":6786},[1977],[1849,6788],{"className":6789,"style":4287},[1981],[1849,6791,1887],{"className":6792},[1990]," 开始的非负检验鞅，那么 Ville 不等式给出：",[1849,6795,6797],{"className":6796},[1852],[1849,6798,6800,6867],{"className":6799},[1856],[1849,6801,6803],{"className":6802},[1860],[1862,6804,6805],{"xmlns":1864,"display":1865},[1867,6806,6807,6864],{},[1870,6808,6809,6819,6858,6860,6862],{},[1878,6810,6811,6813],{},[1881,6812,2544],{},[1878,6814,6815,6817],{},[1881,6816,6288],{},[1885,6818,6192],{},[1870,6820,6821,6823,6842,6848,6850,6856],{},[1873,6822,1876],{"fence":1890},[6824,6825,6826,6834],"munder",{},[1870,6827,6828,6831],{},[1881,6829,6830],{},"sup",[1873,6832,6833],{},"⁡",[1870,6835,6836,6838,6840],{},[1881,6837,2814],{},[1873,6839,2586],{},[1885,6841,6192],{},[1878,6843,6844,6846],{},[1881,6845,6635],{},[1881,6847,2814],{},[1873,6849,2586],{},[5181,6851,6852,6854],{},[1885,6853,1887],{},[1881,6855,2594],{},[1873,6857,1901],{"fence":1890},[1873,6859,5220],{},[1881,6861,2594],{},[1881,6863,1964],{"mathvariant":1963},[1966,6865,6866],{"encoding":1968},"P_{H_0}\\left(\\sup_{t\\ge0}M_t\\ge\\frac{1}{\\alpha}\\right)\\le\\alpha.",[1849,6868,6870,7159],{"className":6869,"ariaHidden":1890},[1973],[1849,6871,6873,6877,6957,6960,7150,7153,7156],{"className":6872},[1977],[1849,6874],{"className":6875,"style":6876},[1981],"height:2.4567em;vertical-align:-1.0067em;",[1849,6878,6880,6883],{"className":6879},[1990],[1849,6881,2544],{"className":6882,"style":2612},[1990,1994],[1849,6884,6886],{"className":6885},[1999],[1849,6887,6889,6949],{"className":6888},[2003,2004],[1849,6890,6892,6946],{"className":6891},[2008],[1849,6893,6895],{"className":6894,"style":6336},[2012],[1849,6896,6897,6900],{"style":5313},[1849,6898],{"className":6899,"style":2021},[2020],[1849,6901,6903],{"className":6902},[2025,2026,2027,2028],[1849,6904,6906],{"className":6905},[1990,2028],[1849,6907,6909,6912],{"className":6908},[1990,2028],[1849,6910,6288],{"className":6911,"style":6354},[1990,1994,2028],[1849,6913,6915],{"className":6914},[1999],[1849,6916,6918,6938],{"className":6917},[2003,2004],[1849,6919,6921,6935],{"className":6920},[2008],[1849,6922,6924],{"className":6923,"style":6367},[2012],[1849,6925,6926,6929],{"style":6370},[1849,6927],{"className":6928,"style":6374},[2020],[1849,6930,6932],{"className":6931},[2025,6378,6379,2028],[1849,6933,6192],{"className":6934},[1990,2028],[1849,6936,2036],{"className":6937},[2035],[1849,6939,6941],{"className":6940},[2008],[1849,6942,6944],{"className":6943,"style":6392},[2012],[1849,6945],{},[1849,6947,2036],{"className":6948},[2035],[1849,6950,6952],{"className":6951},[2008],[1849,6953,6955],{"className":6954,"style":6404},[2012],[1849,6956],{},[1849,6958],{"className":6959,"style":2054},[2053],[1849,6961,6963,6970,7026,7029,7069,7072,7075,7078,7144],{"className":6962},[2110],[1849,6964,6966],{"className":6965,"style":3654},[1986,3653],[1849,6967,1876],{"className":6968},[6969,2027],"delimsizing",[1849,6971,6974],{"className":6972},[5391,6973],"op-limits",[1849,6975,6977,7017],{"className":6976},[2003,2004],[1849,6978,6980,7014],{"className":6979},[2008],[1849,6981,6983,7004],{"className":6982,"style":2775},[2012],[1849,6984,6986,6989],{"style":6985},"top:-2.1885em;margin-left:0em;",[1849,6987],{"className":6988,"style":3047},[2020],[1849,6990,6992],{"className":6991},[2025,2026,2027,2028],[1849,6993,6995,6998,7001],{"className":6994},[1990,2028],[1849,6996,2814],{"className":6997},[1990,1994,2028],[1849,6999,2586],{"className":7000},[2672,2028],[1849,7002,6192],{"className":7003},[1990,2028],[1849,7005,7006,7009],{"style":3043},[1849,7007],{"className":7008,"style":3047},[2020],[1849,7010,7011],{},[1849,7012,6830],{"className":7013},[5391],[1849,7015,2036],{"className":7016},[2035],[1849,7018,7020],{"className":7019},[2008],[1849,7021,7024],{"className":7022,"style":7023},[2012],"height:1.0067em;",[1849,7025],{},[1849,7027],{"className":7028,"style":2054},[2053],[1849,7030,7032,7035],{"className":7031},[1990],[1849,7033,6635],{"className":7034,"style":6661},[1990,1994],[1849,7036,7038],{"className":7037},[1999],[1849,7039,7041,7061],{"className":7040},[2003,2004],[1849,7042,7044,7058],{"className":7043},[2008],[1849,7045,7047],{"className":7046,"style":6223},[2012],[1849,7048,7049,7052],{"style":6676},[1849,7050],{"className":7051,"style":2021},[2020],[1849,7053,7055],{"className":7054},[2025,2026,2027,2028],[1849,7056,2814],{"className":7057},[1990,1994,2028],[1849,7059,2036],{"className":7060},[2035],[1849,7062,7064],{"className":7063},[2008],[1849,7065,7067],{"className":7066,"style":2043},[2012],[1849,7068],{},[1849,7070],{"className":7071,"style":2668},[2053],[1849,7073,2586],{"className":7074},[2672],[1849,7076],{"className":7077,"style":2668},[2053],[1849,7079,7081,7084,7141],{"className":7080},[1990],[1849,7082],{"className":7083},[1986,5365],[1849,7085,7087],{"className":7086},[5181],[1849,7088,7090,7132],{"className":7089},[2003,2004],[1849,7091,7093,7129],{"className":7092},[2008],[1849,7094,7097,7109,7117],{"className":7095,"style":7096},[2012],"height:1.3214em;",[1849,7098,7100,7103],{"style":7099},"top:-2.314em;",[1849,7101],{"className":7102,"style":3047},[2020],[1849,7104,7106],{"className":7105},[1990],[1849,7107,2594],{"className":7108,"style":2779},[1990,1994],[1849,7110,7111,7114],{"style":5504},[1849,7112],{"className":7113,"style":3047},[2020],[1849,7115],{"className":7116,"style":5512},[5511],[1849,7118,7120,7123],{"style":7119},"top:-3.677em;",[1849,7121],{"className":7122,"style":3047},[2020],[1849,7124,7126],{"className":7125},[1990],[1849,7127,1887],{"className":7128},[1990],[1849,7130,2036],{"className":7131},[2035],[1849,7133,7135],{"className":7134},[2008],[1849,7136,7139],{"className":7137,"style":7138},[2012],"height:0.686em;",[1849,7140],{},[1849,7142],{"className":7143},[2100,5365],[1849,7145,7147],{"className":7146,"style":3654},[2100,3653],[1849,7148,1901],{"className":7149},[6969,2027],[1849,7151],{"className":7152,"style":2668},[2053],[1849,7154,5220],{"className":7155},[2672],[1849,7157],{"className":7158,"style":2668},[2053],[1849,7160,7162,7165,7168],{"className":7161},[1977],[1849,7163],{"className":7164,"style":2775},[1981],[1849,7166,2594],{"className":7167,"style":2779},[1990,1994],[1849,7169,1964],{"className":7170},[1990],[1793,7172,7173,7174,7244,7245,7283],{},"把 ",[1849,7175,7177,7195],{"className":7176},[1856],[1849,7178,7180],{"className":7179},[1860],[1862,7181,7182],{"xmlns":1864},[1867,7183,7184,7192],{},[1870,7185,7186],{},[1878,7187,7188,7190],{},[1881,7189,6635],{},[1881,7191,2814],{},[1966,7193,7194],{"encoding":1968},"M_t",[1849,7196,7198],{"className":7197,"ariaHidden":1890},[1973],[1849,7199,7201,7204],{"className":7200},[1977],[1849,7202],{"className":7203,"style":2838},[1981],[1849,7205,7207,7210],{"className":7206},[1990],[1849,7208,6635],{"className":7209,"style":6661},[1990,1994],[1849,7211,7213],{"className":7212},[1999],[1849,7214,7216,7236],{"className":7215},[2003,2004],[1849,7217,7219,7233],{"className":7218},[2008],[1849,7220,7222],{"className":7221,"style":6223},[2012],[1849,7223,7224,7227],{"style":6676},[1849,7225],{"className":7226,"style":2021},[2020],[1849,7228,7230],{"className":7229},[2025,2026,2027,2028],[1849,7231,2814],{"className":7232},[1990,1994,2028],[1849,7234,2036],{"className":7235},[2035],[1849,7237,7239],{"className":7238},[2008],[1849,7240,7242],{"className":7241,"style":2043},[2012],[1849,7243],{}," 想成下注者财富：若原假设正确，任何公平或超公平策略的财富都不应经常膨胀到 ",[1849,7246,7248,7267],{"className":7247},[1856],[1849,7249,7251],{"className":7250},[1860],[1862,7252,7253],{"xmlns":1864},[1867,7254,7255,7264],{},[1870,7256,7257,7259,7262],{},[1885,7258,1887],{},[1881,7260,7261],{"mathvariant":1963},"\u002F",[1881,7263,2594],{},[1966,7265,7266],{"encoding":1968},"1\u002F\\alpha",[1849,7268,7270],{"className":7269,"ariaHidden":1890},[1973],[1849,7271,7273,7276,7280],{"className":7272},[1977],[1849,7274],{"className":7275,"style":1982},[1981],[1849,7277,7279],{"className":7278},[1990],"1\u002F",[1849,7281,2594],{"className":7282,"style":2779},[1990,1994],"。因此研究者可以持续监测，并在财富首次超过阈值时停止。",[1841,7285,7287],{"id":7286},"_3-置信序列","3. 置信序列",[1793,7289,7290,7291,7319,7320,7401],{},"固定样本置信区间只保证某个预定 ",[1849,7292,7294,7307],{"className":7293},[1856],[1849,7295,7297],{"className":7296},[1860],[1862,7298,7299],{"xmlns":1864},[1867,7300,7301,7305],{},[1870,7302,7303],{},[1881,7304,1917],{},[1966,7306,1917],{"encoding":1968},[1849,7308,7310],{"className":7309,"ariaHidden":1890},[1973],[1849,7311,7313,7316],{"className":7312},[1977],[1849,7314],{"className":7315,"style":2775},[1981],[1849,7317,1917],{"className":7318},[1990,1994]," 的覆盖。置信序列 ",[1849,7321,7323,7345],{"className":7322},[1856],[1849,7324,7326],{"className":7325},[1860],[1862,7327,7328],{"xmlns":1864},[1867,7329,7330,7342],{},[1870,7331,7332,7334,7340],{},[1873,7333,1876],{"stretchy":1875},[1878,7335,7336,7338],{},[1881,7337,2438],{},[1881,7339,2814],{},[1873,7341,1901],{"stretchy":1875},[1966,7343,7344],{"encoding":1968},"(C_t)",[1849,7346,7348],{"className":7347,"ariaHidden":1890},[1973],[1849,7349,7351,7354,7357,7398],{"className":7350},[1977],[1849,7352],{"className":7353,"style":1982},[1981],[1849,7355,1876],{"className":7356},[1986],[1849,7358,7360,7363],{"className":7359},[1990],[1849,7361,2438],{"className":7362,"style":2470},[1990,1994],[1849,7364,7366],{"className":7365},[1999],[1849,7367,7369,7390],{"className":7368},[2003,2004],[1849,7370,7372,7387],{"className":7371},[2008],[1849,7373,7375],{"className":7374,"style":6223},[2012],[1849,7376,7378,7381],{"style":7377},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[1849,7379],{"className":7380,"style":2021},[2020],[1849,7382,7384],{"className":7383},[2025,2026,2027,2028],[1849,7385,2814],{"className":7386},[1990,1994,2028],[1849,7388,2036],{"className":7389},[2035],[1849,7391,7393],{"className":7392},[2008],[1849,7394,7396],{"className":7395,"style":2043},[2012],[1849,7397],{},[1849,7399,1901],{"className":7400},[2100]," 则满足：",[1849,7403,7405],{"className":7404},[1852],[1849,7406,7408,7457],{"className":7407},[1856],[1849,7409,7411],{"className":7410},[1860],[1862,7412,7413],{"xmlns":1864,"display":1865},[1867,7414,7415,7454],{},[1870,7416,7417,7419,7421,7424,7426,7432,7436,7438,7440,7442,7444,7446,7448,7450,7452],{},[1881,7418,2544],{},[1873,7420,2547],{"stretchy":1875},[1881,7422,7423],{},"θ",[1873,7425,2562],{},[1878,7427,7428,7430],{},[1881,7429,2438],{},[1881,7431,2814],{},[7433,7434,7435],"mtext",{}," 对所有 ",[1881,7437,2814],{},[1873,7439,2586],{},[1885,7441,1887],{},[1873,7443,2583],{"stretchy":1875},[1873,7445,2586],{},[1885,7447,1887],{},[1873,7449,2591],{},[1881,7451,2594],{},[1881,7453,1964],{"mathvariant":1963},[1966,7455,7456],{"encoding":1968},"P\\{\\theta\\in C_t\\ \\text{对所有 }t\\ge1\\}\\ge1-\\alpha.",[1849,7458,7460,7484,7558,7579,7597],{"className":7459,"ariaHidden":1890},[1973],[1849,7461,7463,7466,7469,7472,7475,7478,7481],{"className":7462},[1977],[1849,7464],{"className":7465,"style":1982},[1981],[1849,7467,2544],{"className":7468,"style":2612},[1990,1994],[1849,7470,2547],{"className":7471},[1986],[1849,7473,7423],{"className":7474,"style":2875},[1990,1994],[1849,7476],{"className":7477,"style":2668},[2053],[1849,7479,2562],{"className":7480},[2672],[1849,7482],{"className":7483,"style":2668},[2053],[1849,7485,7487,7490,7530,7534,7546,7549,7552,7555],{"className":7486},[1977],[1849,7488],{"className":7489,"style":2838},[1981],[1849,7491,7493,7496],{"className":7492},[1990],[1849,7494,2438],{"className":7495,"style":2470},[1990,1994],[1849,7497,7499],{"className":7498},[1999],[1849,7500,7502,7522],{"className":7501},[2003,2004],[1849,7503,7505,7519],{"className":7504},[2008],[1849,7506,7508],{"className":7507,"style":6223},[2012],[1849,7509,7510,7513],{"style":7377},[1849,7511],{"className":7512,"style":2021},[2020],[1849,7514,7516],{"className":7515},[2025,2026,2027,2028],[1849,7517,2814],{"className":7518},[1990,1994,2028],[1849,7520,2036],{"className":7521},[2035],[1849,7523,7525],{"className":7524},[2008],[1849,7526,7528],{"className":7527,"style":2043},[2012],[1849,7529],{},[1849,7531,7533],{"className":7532},[2053]," ",[1849,7535,7538,7543],{"className":7536},[1990,7537],"text",[1849,7539,7542],{"className":7540},[1990,7541],"cjk_fallback","对所有",[1849,7544,7533],{"className":7545},[1990],[1849,7547,2814],{"className":7548},[1990,1994],[1849,7550],{"className":7551,"style":2668},[2053],[1849,7553,2586],{"className":7554},[2672],[1849,7556],{"className":7557,"style":2668},[2053],[1849,7559,7561,7564,7567,7570,7573,7576],{"className":7560},[1977],[1849,7562],{"className":7563,"style":1982},[1981],[1849,7565,1887],{"className":7566},[1990],[1849,7568,2583],{"className":7569},[2100],[1849,7571],{"className":7572,"style":2668},[2053],[1849,7574,2586],{"className":7575},[2672],[1849,7577],{"className":7578,"style":2668},[2053],[1849,7580,7582,7585,7588,7591,7594],{"className":7581},[1977],[1849,7583],{"className":7584,"style":2756},[1981],[1849,7586,1887],{"className":7587},[1990],[1849,7589],{"className":7590,"style":2061},[2053],[1849,7592,2591],{"className":7593},[2257],[1849,7595],{"className":7596,"style":2061},[2053],[1849,7598,7600,7603,7606],{"className":7599},[1977],[1849,7601],{"className":7602,"style":2775},[1981],[1849,7604,2594],{"className":7605,"style":2779},[1990,1994],[1849,7607,1964],{"className":7608},[1990],[1793,7610,7611],{},"它允许在任意时刻报告区间，但通常比只针对一个固定时点优化的区间更宽。这是灵活停止的价格。",[1841,7613,7615],{"id":7614},"_4-使用边界","4. 使用边界",[5049,7617,7618,7621,7624,7627],{},[1815,7619,7620],{},"“随时有效”不是“任何分析选择都有效”；临时更换终点、亚组或下注策略仍需被框架覆盖。",[1815,7622,7623],{},"e-value 不是效果大小；它衡量证据，不说明处理是否具有实质意义。",[1815,7625,7626],{},"多个 e-value 可以按特定规则组合，但不能把普通 p 值随意相乘后称为 e-process。",[1815,7628,7629],{},"置信序列仍依赖数据界、条件矩或模型假设。",[1805,7631,7633],{"id":7632},"浏览器实验交换性与分布漂移下的保形覆盖率","浏览器实验：交换性与分布漂移下的保形覆盖率",[1793,7635,7636,7637,7724,7725,7772,7773,7853],{},"训练与校准数据来自 ",[1849,7638,7640,7673],{"className":7639},[1856],[1849,7641,7643],{"className":7642},[1860],[1862,7644,7645],{"xmlns":1864},[1867,7646,7647,7670],{},[1870,7648,7649,7651,7654,7657,7659,7661,7664,7666,7668],{},[1881,7650,1883],{},[1873,7652,7653],{},"∼",[1881,7655,7656],{},"U",[1873,7658,3857],{"stretchy":1875},[1873,7660,2591],{},[1885,7662,7663],{},"2",[1873,7665,1891],{"separator":1890},[1885,7667,7663],{},[1873,7669,3902],{"stretchy":1875},[1966,7671,7672],{"encoding":1968},"X\\sim U[-2,2]",[1849,7674,7676,7694],{"className":7675,"ariaHidden":1890},[1973],[1849,7677,7679,7682,7685,7688,7691],{"className":7678},[1977],[1849,7680],{"className":7681,"style":5905},[1981],[1849,7683,1883],{"className":7684,"style":1995},[1990,1994],[1849,7686],{"className":7687,"style":2668},[2053],[1849,7689,7653],{"className":7690},[2672],[1849,7692],{"className":7693,"style":2668},[2053],[1849,7695,7697,7700,7703,7706,7709,7712,7715,7718,7721],{"className":7696},[1977],[1849,7698],{"className":7699,"style":1982},[1981],[1849,7701,7656],{"className":7702,"style":6661},[1990,1994],[1849,7704,3857],{"className":7705},[1986],[1849,7707,2591],{"className":7708},[1990],[1849,7710,7663],{"className":7711},[1990],[1849,7713,1891],{"className":7714},[2049],[1849,7716],{"className":7717,"style":2054},[2053],[1849,7719,7663],{"className":7720},[1990],[1849,7722,3902],{"className":7723},[2100],"，结果为 ",[1849,7726,7728,7751],{"className":7727},[1856],[1849,7729,7731],{"className":7730},[1860],[1862,7732,7733],{"xmlns":1864},[1867,7734,7735,7748],{},[1870,7736,7737,7740,7742,7744,7746],{},[1881,7738,7739],{},"sin",[1873,7741,6833],{},[1873,7743,1876],{"stretchy":1875},[1881,7745,1883],{},[1873,7747,1901],{"stretchy":1875},[1966,7749,7750],{"encoding":1968},"\\sin(X)",[1849,7752,7754],{"className":7753,"ariaHidden":1890},[1973],[1849,7755,7757,7760,7763,7766,7769],{"className":7756},[1977],[1849,7758],{"className":7759,"style":1982},[1981],[1849,7761,7739],{"className":7762},[5391],[1849,7764,1876],{"className":7765},[1986],[1849,7767,1883],{"className":7768,"style":1995},[1990,1994],[1849,7770,1901],{"className":7771},[2100]," 加噪声。我们故意用二次多项式拟合。第一组测试数据与校准数据同分布；第二组来自 ",[1849,7774,7776,7805],{"className":7775},[1856],[1849,7777,7779],{"className":7778},[1860],[1862,7780,7781],{"xmlns":1864},[1867,7782,7783,7802],{},[1870,7784,7785,7787,7789,7791,7793,7795,7797,7800],{},[1881,7786,1883],{},[1873,7788,7653],{},[1881,7790,7656],{},[1873,7792,3857],{"stretchy":1875},[1885,7794,7663],{},[1873,7796,1891],{"separator":1890},[1885,7798,7799],{},"4",[1873,7801,3902],{"stretchy":1875},[1966,7803,7804],{"encoding":1968},"X\\sim U[2,4]",[1849,7806,7808,7826],{"className":7807,"ariaHidden":1890},[1973],[1849,7809,7811,7814,7817,7820,7823],{"className":7810},[1977],[1849,7812],{"className":7813,"style":5905},[1981],[1849,7815,1883],{"className":7816,"style":1995},[1990,1994],[1849,7818],{"className":7819,"style":2668},[2053],[1849,7821,7653],{"className":7822},[2672],[1849,7824],{"className":7825,"style":2668},[2053],[1849,7827,7829,7832,7835,7838,7841,7844,7847,7850],{"className":7828},[1977],[1849,7830],{"className":7831,"style":1982},[1981],[1849,7833,7656],{"className":7834,"style":6661},[1990,1994],[1849,7836,3857],{"className":7837},[1986],[1849,7839,7663],{"className":7840},[1990],[1849,7842,1891],{"className":7843},[2049],[1849,7845],{"className":7846,"style":2054},[2053],[1849,7848,7799],{"className":7849},[1990],[1849,7851,3902],{"className":7852},[2100],"，进入训练数据很少覆盖的区域。传统 split conformal 的区间宽度不随位置改变，因此漂移后可能覆盖不足。",[7855,7856],"pyodide",{"code64":7857,"layout":7858,"locale":7,"packages":7859,"title":7860},"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","vertical","numpy","Python：Split conformal 的覆盖率与分布漂移",[7862,7863],"web-r",{"code64":7864,"layout":7858,"locale":7,"title":7865},"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","R：Split conformal 的覆盖率与分布漂移",[1841,7867,7868],{"id":7868},"实验审计",[5049,7870,7871,7874,7877,7920],{},[1815,7872,7873],{},"把模型从二次多项式改为一次和五次，比较覆盖率与区间宽度；覆盖有效不代表宽度相同。",[1815,7875,7876],{},"把校准样本从 250 降到 30，观察分位数更离散。",[1815,7878,7879,7880,7919],{},"让噪声标准差随 ",[1849,7881,7883,7901],{"className":7882},[1856],[1849,7884,7886],{"className":7885},[1860],[1862,7887,7888],{"xmlns":1864},[1867,7889,7890,7898],{},[1870,7891,7892,7894,7896],{},[1881,7893,3126],{"mathvariant":1963},[1881,7895,1883],{},[1881,7897,3126],{"mathvariant":1963},[1966,7899,7900],{"encoding":1968},"|X|",[1849,7902,7904],{"className":7903,"ariaHidden":1890},[1973],[1849,7905,7907,7910,7913,7916],{"className":7906},[1977],[1849,7908],{"className":7909,"style":1982},[1981],[1849,7911,3126],{"className":7912},[1990],[1849,7914,1883],{"className":7915,"style":1995},[1990,1994],[1849,7917,3126],{"className":7918},[1990]," 增加，检查固定宽度区间在哪些区域覆盖不足。",[1815,7921,7922],{},"漂移测试不满足经典保证，因此低覆盖不是 conformal 定理“出错”，而是其假设被破坏。",[1805,7924,7926],{"id":7925},"浏览器实验二总体覆盖达标高风险组仍可能失准","浏览器实验二：总体覆盖达标，高风险组仍可能失准",[1793,7928,7929,7930,7958],{},"结果均值恒为 0，但噪声随风险分数 ",[1849,7931,7933,7946],{"className":7932},[1856],[1849,7934,7936],{"className":7935},[1860],[1862,7937,7938],{"xmlns":1864},[1867,7939,7940,7944],{},[1870,7941,7942],{},[1881,7943,1883],{},[1966,7945,1883],{"encoding":1968},[1849,7947,7949],{"className":7948,"ariaHidden":1890},[1973],[1849,7950,7952,7955],{"className":7951},[1977],[1849,7953],{"className":7954,"style":5905},[1981],[1849,7956,1883],{"className":7957,"style":1995},[1990,1994]," 增大。全局 split conformal 用一条固定半宽区间达到约 90% 的边际覆盖；随后只选择风险最高的 10% 对象，检查其覆盖。",[7855,7960],{"code64":7961,"layout":7858,"locale":7,"packages":7859,"title":7962},"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","Python：边际覆盖与选择条件覆盖",[1793,7964,7965],{},"低覆盖不是 split conformal 定理失效：总体测试点与校准点仍同分布，边际目标确实接近 90%。问题在于选择规则把注意力集中到高噪声区域，改变了要保证的条件事件。",[1805,7967,7968],{"id":7968},"分层作业",[1841,7970,7971],{"id":7971},"本科生任务",[1793,7973,7974],{},"用 100 次完整重复实验估计 split conformal 的平均覆盖率。每次都必须重新生成训练、校准和测试数据。分别报告总体与 top-10% 风险组覆盖，并解释为什么两者可以不同。",[1841,7976,7977],{"id":7977},"研究生任务",[1793,7979,7980],{},"为连续监测的 A\u002FB 测试写一份推断协议：声明原假设、最大或无限时域、下注\u002Fe-process 构造、停止阈值、效果大小区间和实际最小重要差异。再比较固定样本设计、alpha spending 与置信序列在样本效率和运营灵活性上的权衡。",[1805,7982,7983],{"id":7983},"一手文献与延伸阅读",[1812,7985,7986,8000,8017,8033,8044],{},[1815,7987,7988,7989,7995,7996,7999],{},"Angelopoulos, A. N., & Bates, S. (2023). ",[2820,7990,7994],{"href":7991,"rel":7992},"https:\u002F\u002Fdoi.org\u002F10.1561\u002F2200000101",[7993],"nofollow","Conformal Prediction: A Gentle Introduction",". ",[5847,7997,7998],{},"Foundations and Trends in Machine Learning",", 16(4), 494–591.",[1815,8001,8002,8003,7995,8008,8011,8012,1964],{},"Barber, R. F., Candès, E. J., Ramdas, A., & Tibshirani, R. J. (2023). ",[2820,8004,8007],{"href":8005,"rel":8006},"https:\u002F\u002Fprojecteuclid.org\u002Fjournals\u002Fannals-of-statistics\u002Fvolume-51\u002Fissue-2\u002FConformal-prediction-beyond-exchangeability\u002F10.1214\u002F23-AOS2276.full",[7993],"Conformal Prediction Beyond Exchangeability",[5847,8009,8010],{},"Annals of Statistics",", 51(2), 816–845. DOI: ",[2820,8013,8016],{"href":8014,"rel":8015},"https:\u002F\u002Fdoi.org\u002F10.1214\u002F23-AOS2276",[7993],"10.1214\u002F23-AOS2276",[1815,8018,8019,8020,7995,8025,8027,8028,1964],{},"Jin, Y., & Ren, Z. (2025). ",[2820,8021,8024],{"href":8022,"rel":8023},"https:\u002F\u002Facademic.oup.com\u002Fjrsssb\u002Farticle\u002F87\u002F4\u002F1239\u002F8113856",[7993],"Confidence on the Focal: Conformal Prediction with Selection-Conditional Coverage",[5847,8026,5877],{},", 87(4), 1239–1259. DOI: ",[2820,8029,8032],{"href":8030,"rel":8031},"https:\u002F\u002Fdoi.org\u002F10.1093\u002Fjrsssb\u002Fqkaf016",[7993],"10.1093\u002Fjrsssb\u002Fqkaf016",[1815,8034,8035,8036,7995,8041,8043],{},"Zhang, C., Li, T., Xie, J., Kong, L., & Jiang, B. (2026). ",[2820,8037,8040],{"href":8038,"rel":8039},"https:\u002F\u002Fjmlr.org\u002Fpapers\u002Fv27\u002F24-1899.html",[7993],"Transfer Conformal Predictive Inference for Regression",[5847,8042,5849],{},", 27(90), 1–68.",[1815,8045,8046,8047,7995,8052,8055],{},"Ramdas, A., Grünwald, P., Vovk, V., & Shafer, G. (2023). ",[2820,8048,8051],{"href":8049,"rel":8050},"https:\u002F\u002Fdoi.org\u002F10.1214\u002F23-STS894",[7993],"Game-Theoretic Statistics and Safe Anytime-Valid Inference",[5847,8053,8054],{},"Statistical Science",", 38(4), 576–601.",[1793,8057,8058,8059,8063,8064,8068,8069,8073],{},"建议与",[2820,8060,8062],{"href":8061},".\u002F01-probability\u002F05-asymptotics\u002F","渐近理论","、",[2820,8065,8067],{"href":8066},".\u002F02-statistics\u002F02-interval-estimation\u002F","区间估计","和",[2820,8070,8072],{"href":8071},".\u002F02-statistics\u002F07-bootstrap\u002F","Bootstrap","对照学习：它们都在量化不确定性，但依赖的重复抽样结构和有效性目标并不相同。",{"title":10,"searchDepth":8075,"depth":8075,"links":8076},2,[8077,8078,8085,8091,8092,8098,8101,8102,8106],{"id":1807,"depth":8075,"text":1807},{"id":1838,"depth":8075,"text":1839,"children":8079},[8080,8082,8083,8084],{"id":1843,"depth":8081,"text":1844},3,{"id":2788,"depth":8081,"text":2789},{"id":4294,"depth":8081,"text":4295},{"id":4488,"depth":8081,"text":4489},{"id":5039,"depth":8075,"text":5040,"children":8086},[8087,8088,8089,8090],{"id":5043,"depth":8081,"text":5044},{"id":5068,"depth":8081,"text":5069},{"id":5818,"depth":8081,"text":5819},{"id":5841,"depth":8081,"text":5842},{"id":5867,"depth":8075,"text":5868},{"id":6066,"depth":8075,"text":6067,"children":8093},[8094,8095,8096,8097],{"id":6070,"depth":8081,"text":6071},{"id":6164,"depth":8081,"text":6165},{"id":7286,"depth":8081,"text":7287},{"id":7614,"depth":8081,"text":7615},{"id":7632,"depth":8075,"text":7633,"children":8099},[8100],{"id":7868,"depth":8081,"text":7868},{"id":7925,"depth":8075,"text":7926},{"id":7968,"depth":8075,"text":7968,"children":8103},[8104,8105],{"id":7971,"depth":8081,"text":7971},{"id":7977,"depth":8081,"text":7977},{"id":7983,"depth":8075,"text":7983},"从保形预测、分布漂移与随时有效推断理解现代不确定性量化的保证、假设和边界。","md",{"sidebar":8110},{"order":8111},14,true,{"title":1728,"description":8107},"pxQqBdajnTThyQXnXaQhMvTl7XET5tvZGJCVyOTfHMQ",[8116,8118],{"title":1722,"path":1723,"stem":1724,"description":8117,"children":-1},"从经验分布出发构造标准误与区间，比较 percentile、basic、BCa、参数和块 Bootstrap。",{"title":1737,"path":1738,"stem":1739,"description":8119,"children":-1},"一门以时点数据、样本外证据、交易成本和可复现研究为主线的量化投资课程。",1785754757705]