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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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",[1840,3429,3431,3471],{"className":3430},[1847],[1840,3432,3434],{"className":3433},[1851],[1853,3435,3436],{"xmlns":1855},[1858,3437,3438,3468],{},[1861,3439,3440,3443,3445,3447,3449,3451,3454,3456,3459,3461,3463,3465],{},[1867,3441,3442],{},"U",[1874,3444,1888],{"stretchy":1876},[1867,3446,1872],{},[1874,3448,1894],{"stretchy":1876},[1874,3450,1900],{},[1867,3452,3453],{"mathvariant":2283},"∂",[1867,3455,2680],{"mathvariant":2283},[1867,3457,3458],{"mathvariant":2283},"\u002F",[1867,3460,3453],{"mathvariant":2283},[1867,3462,1872],{},[1874,3464,1900],{},[1927,3466,3467],{},"0",[1943,3469,3470],{"encoding":1945},"U(\\theta)=\\partial\\ell\u002F\\partial\\theta=0",[1840,3472,3474,3501,3532],{"className":3473,"ariaHidden":1916},[1950],[1840,3475,3477,3480,3483,3486,3489,3492,3495,3498],{"className":3476},[1954],[1840,3478],{"className":3479,"style":2739},[1958],[1840,3481,3442],{"className":3482,"style":3297},[1963,1967],[1840,3484,1888],{"className":3485},[2023],[1840,3487,1872],{"className":3488,"style":2005},[1963,1967],[1840,3490,1894],{"className":3491},[2079],[1840,3493],{"className":3494,"style":2084},[1919],[1840,3496,1900],{"className":3497},[2088],[1840,3499],{"className":3500,"style":2084},[1919],[1840,3502,3504,3507,3511,3514,3517,3520,3523,3526,3529],{"className":3503},[1954],[1840,3505],{"className":3506,"style":2739},[1958],[1840,3508,3453],{"className":3509,"style":3510},[1963],"margin-right:0.0556em;",[1840,3512,2680],{"className":3513},[1963],[1840,3515,3458],{"className":3516},[1963],[1840,3518,3453],{"className":3519,"style":3510},[1963],[1840,3521,1872],{"className":3522,"style":2005},[1963,1967],[1840,3524],{"className":3525,"style":2084},[1919],[1840,3527,1900],{"className":3528},[2088],[1840,3530],{"className":3531,"style":2084},[1919],[1840,3533,3535,3539],{"className":3534},[1954],[1840,3536],{"className":3537,"style":3538},[1958],"height:0.6444em;",[1840,3540,3467],{"className":3541},[1963],"；",[1817,3544,3545],{},"检查边界、二阶条件和全局最大值；",[1817,3547,3548],{},"用信息矩阵或 profile likelihood 量化不确定性。",[1796,3550,3551],{},"MLE 具有变换不变性，但有限样本可有偏；混合模型、分离 Logit 和方差边界会出现非正则问题。",[1807,3553,3555],{"id":3554},"_3-贝叶斯估计","3. 贝叶斯估计",[1840,3557,3559],{"className":3558},[1843],[1840,3560,3562,3613],{"className":3561},[1847],[1840,3563,3565],{"className":3564},[1851],[1853,3566,3567],{"xmlns":1855,"display":1856},[1858,3568,3569,3610],{},[1861,3570,3571,3574,3576,3578,3581,3583,3585,3588,3590,3592,3594,3596,3598,3600,3602,3604,3606,3608],{},[1867,3572,3573],{},"π",[1874,3575,1888],{"stretchy":1876},[1867,3577,1872],{},[1874,3579,3580],{},"∣",[1867,3582,2637],{},[1874,3584,1894],{"stretchy":1876},[1874,3586,3587],{},"∝",[1867,3589,2627],{},[1874,3591,1888],{"stretchy":1876},[1867,3593,1872],{},[1874,3595,2634],{"separator":1916},[1867,3597,2637],{},[1874,3599,1894],{"stretchy":1876},[1867,3601,3573],{},[1874,3603,1888],{"stretchy":1876},[1867,3605,1872],{},[1874,3607,1894],{"stretchy":1876},[1867,3609,2284],{"mathvariant":2283},[1943,3611,3612],{"encoding":1945},"\\pi(\\theta\\mid x)\n\\propto L(\\theta;x)\\pi(\\theta).",[1840,3614,3616,3640,3661],{"className":3615,"ariaHidden":1916},[1950],[1840,3617,3619,3622,3625,3628,3631,3634,3637],{"className":3618},[1954],[1840,3620],{"className":3621,"style":2739},[1958],[1840,3623,3573],{"className":3624,"style":2030},[1963,1967],[1840,3626,1888],{"className":3627},[2023],[1840,3629,1872],{"className":3630,"style":2005},[1963,1967],[1840,3632],{"className":3633,"style":2084},[1919],[1840,3635,3580],{"className":3636},[2088],[1840,3638],{"className":3639,"style":2084},[1919],[1840,3641,3643,3646,3649,3652,3655,3658],{"className":3642},[1954],[1840,3644],{"className":3645,"style":2739},[1958],[1840,3647,2637],{"className":3648},[1963,1967],[1840,3650,1894],{"className":3651},[2079],[1840,3653],{"className":3654,"style":2084},[1919],[1840,3656,3587],{"className":3657},[2088],[1840,3659],{"className":3660,"style":2084},[1919],[1840,3662,3664,3667,3670,3673,3676,3679,3682,3685,3688,3691,3694,3697,3700],{"className":3663},[1954],[1840,3665],{"className":3666,"style":2739},[1958],[1840,3668,2627],{"className":3669},[1963,1967],[1840,3671,1888],{"className":3672},[2023],[1840,3674,1872],{"className":3675,"style":2005},[1963,1967],[1840,3677,2634],{"className":3678},[2151],[1840,3680],{"className":3681,"style":2159},[1919],[1840,3683,2637],{"className":3684},[1963,1967],[1840,3686,1894],{"className":3687},[2079],[1840,3689,3573],{"className":3690,"style":2030},[1963,1967],[1840,3692,1888],{"className":3693},[2023],[1840,3695,1872],{"className":3696,"style":2005},[1963,1967],[1840,3698,1894],{"className":3699},[2079],[1840,3701,2284],{"className":3702},[1963],[1796,3704,3705],{},"点估计取决于损失：",[3707,3708,3709,3722],"table",{},[3710,3711,3712],"thead",{},[3713,3714,3715,3719],"tr",{},[3716,3717,3718],"th",{},"损失",[3716,3720,3721],{},"Bayes 估计",[3723,3724,3725,3734,3742],"tbody",{},[3713,3726,3727,3731],{},[3728,3729,3730],"td",{},"平方损失",[3728,3732,3733],{},"后验均值",[3713,3735,3736,3739],{},[3728,3737,3738],{},"绝对损失",[3728,3740,3741],{},"后验中位数",[3713,3743,3744,3747],{},[3728,3745,3746],{},"0–1 类损失",[3728,3748,3749],{},"后验众数 \u002F MAP",[1796,3751,3752],{},"MAP 不是“贝叶斯版 MLE”的全部；完整贝叶斯推断以整个后验分布表达不确定性。",[1807,3754,3756],{"id":3755},"_4-可运行案例泊松率的-mle-与-gammapoisson-收缩","4. 可运行案例：泊松率的 MLE 与 Gamma–Poisson 收缩",[1796,3758,3759,3760,3899,3900,3966,3967,4062,4063,4091],{},"若 ",[1840,3761,3763,3808],{"className":3762},[1847],[1840,3764,3766],{"className":3765},[1851],[1853,3767,3768],{"xmlns":1855},[1858,3769,3770,3805],{},[1861,3771,3772,3778,3781,3784,3787,3789,3792,3794,3796,3798,3800,3803],{},[1864,3773,3774,3776],{},[1867,3775,1891],{},[1867,3777,2244],{},[1874,3779,3780],{},"∼",[1867,3782,3783],{},"P",[1867,3785,3786],{},"o",[1867,3788,2244],{},[1867,3790,3791],{},"s",[1867,3793,3791],{},[1867,3795,3786],{},[1867,3797,2233],{},[1874,3799,1888],{"stretchy":1876},[1867,3801,3802],{},"λ",[1874,3804,1894],{"stretchy":1876},[1943,3806,3807],{"encoding":1945},"X_i\\sim Poisson(\\lambda)",[1840,3809,3811,3867],{"className":3810,"ariaHidden":1916},[1950],[1840,3812,3814,3818,3858,3861,3864],{"className":3813},[1954],[1840,3815],{"className":3816,"style":3817},[1958],"height:0.8333em;vertical-align:-0.15em;",[1840,3819,3821,3824],{"className":3820},[1963],[1840,3822,1891],{"className":3823,"style":2075},[1963,1967],[1840,3825,3827],{"className":3826},[1972],[1840,3828,3830,3850],{"className":3829},[1976,1977],[1840,3831,3833,3847],{"className":3832},[1981],[1840,3834,3836],{"className":3835,"style":2043},[1985],[1840,3837,3838,3841],{"style":2512},[1840,3839],{"className":3840,"style":1994},[1993],[1840,3842,3844],{"className":3843},[1998,1999,2000,2001],[1840,3845,2244],{"className":3846},[1963,1967,2001],[1840,3848,2010],{"className":3849},[2009],[1840,3851,3853],{"className":3852},[1981],[1840,3854,3856],{"className":3855,"style":2017},[1985],[1840,3857],{},[1840,3859],{"className":3860,"style":2084},[1919],[1840,3862,3780],{"className":3863},[2088],[1840,3865],{"className":3866,"style":2084},[1919],[1840,3868,3870,3873,3877,3880,3883,3887,3890,3893,3896],{"className":3869},[1954],[1840,3871],{"className":3872,"style":2739},[1958],[1840,3874,3783],{"className":3875,"style":3876},[1963,1967],"margin-right:0.1389em;",[1840,3878,3786],{"className":3879},[1963,1967],[1840,3881,2244],{"className":3882},[1963,1967],[1840,3884,3886],{"className":3885},[1963,1967],"sso",[1840,3888,2233],{"className":3889},[1963,1967],[1840,3891,1888],{"className":3892},[2023],[1840,3894,3802],{"className":3895},[1963,1967],[1840,3897,1894],{"className":3898},[2079],"，矩估计与 MLE 都是 ",[1840,3901,3903,3922],{"className":3902},[1847],[1840,3904,3906],{"className":3905},[1851],[1853,3907,3908],{"xmlns":1855},[1858,3909,3910,3919],{},[1861,3911,3912],{},[3154,3913,3914,3916],{"accent":1916},[1867,3915,1891],{},[1874,3917,3918],{},"ˉ",[1943,3920,3921],{"encoding":1945},"\\bar X",[1840,3923,3925],{"className":3924,"ariaHidden":1916},[1950],[1840,3926,3928,3932],{"className":3927},[1954],[1840,3929],{"className":3930,"style":3931},[1958],"height:0.8201em;",[1840,3933,3935],{"className":3934},[1963,3226],[1840,3936,3938],{"className":3937},[1976],[1840,3939,3941],{"className":3940},[1981],[1840,3942,3944,3952],{"className":3943,"style":3931},[1985],[1840,3945,3946,3949],{"style":3239},[1840,3947],{"className":3948,"style":2324},[1993],[1840,3950,1891],{"className":3951,"style":2075},[1963,1967],[1840,3953,3955,3958],{"style":3954},"top:-3.2523em;",[1840,3956],{"className":3957,"style":2324},[1993],[1840,3959,3963],{"className":3960,"style":3962},[3961],"accent-body","left:-0.1667em;",[1840,3964,3918],{"className":3965},[1963],"。设先验 ",[1840,3968,3970,4009],{"className":3969},[1847],[1840,3971,3973],{"className":3972},[1851],[1853,3974,3975],{"xmlns":1855},[1858,3976,3977,4006],{},[1861,3978,3979,3981,3983,3986,3989,3991,3993,3995,3997,3999,4001,4004],{},[1867,3980,3802],{},[1874,3982,3780],{},[1867,3984,3985],{},"G",[1867,3987,3988],{},"a",[1867,3990,1905],{},[1867,3992,1905],{},[1867,3994,3988],{},[1874,3996,1888],{"stretchy":1876},[1867,3998,3988],{},[1874,4000,1917],{"separator":1916},[1867,4002,4003],{},"b",[1874,4005,1894],{"stretchy":1876},[1943,4007,4008],{"encoding":1945},"\\lambda\\sim Gamma(a,b)",[1840,4010,4012,4031],{"className":4011,"ariaHidden":1916},[1950],[1840,4013,4015,4019,4022,4025,4028],{"className":4014},[1954],[1840,4016],{"className":4017,"style":4018},[1958],"height:0.6944em;",[1840,4020,3802],{"className":4021},[1963,1967],[1840,4023],{"className":4024,"style":2084},[1919],[1840,4026,3780],{"className":4027},[2088],[1840,4029],{"className":4030,"style":2084},[1919],[1840,4032,4034,4037,4040,4044,4047,4050,4053,4056,4059],{"className":4033},[1954],[1840,4035],{"className":4036,"style":2739},[1958],[1840,4038,3985],{"className":4039},[1963,1967],[1840,4041,4043],{"className":4042},[1963,1967],"amma",[1840,4045,1888],{"className":4046},[2023],[1840,4048,3988],{"className":4049},[1963,1967],[1840,4051,1917],{"className":4052},[2151],[1840,4054],{"className":4055,"style":2159},[1919],[1840,4057,4003],{"className":4058},[1963,1967],[1840,4060,1894],{"className":4061},[2079],"（",[1840,4064,4066,4079],{"className":4065},[1847],[1840,4067,4069],{"className":4068},[1851],[1853,4070,4071],{"xmlns":1855},[1858,4072,4073,4077],{},[1861,4074,4075],{},[1867,4076,4003],{},[1943,4078,4003],{"encoding":1945},[1840,4080,4082],{"className":4081,"ariaHidden":1916},[1950],[1840,4083,4085,4088],{"className":4084},[1954],[1840,4086],{"className":4087,"style":4018},[1958],[1840,4089,4003],{"className":4090},[1963,1967]," 为 rate），后验均值为：",[1840,4093,4095],{"className":4094},[1843],[1840,4096,4098,4155],{"className":4097},[1847],[1840,4099,4101],{"className":4100},[1851],[1853,4102,4103],{"xmlns":1855,"display":1856},[1858,4104,4105,4152],{},[1861,4106,4107,4109,4111,4113,4115,4117,4119,4121,4150],{},[1867,4108,1869],{},[1874,4110,1877],{"stretchy":1876},[1867,4112,3802],{},[1874,4114,3580],{},[1867,4116,1891],{},[1874,4118,1897],{"stretchy":1876},[1874,4120,1900],{},[2227,4122,4123,4142],{},[1861,4124,4125,4127,4130,4136],{},[1867,4126,3988],{},[1874,4128,4129],{},"+",[3178,4131,4132,4134],{},[1874,4133,2239],{},[1867,4135,2244],{},[1864,4137,4138,4140],{},[1867,4139,1891],{},[1867,4141,2244],{},[1861,4143,4144,4146,4148],{},[1867,4145,4003],{},[1874,4147,4129],{},[1867,4149,2233],{},[1867,4151,2284],{"mathvariant":2283},[1943,4153,4154],{"encoding":1945},"E[\\lambda\\mid X]\n=\\frac{a+\\sum_iX_i}{b+n}.",[1840,4156,4158,4182,4203],{"className":4157,"ariaHidden":1916},[1950],[1840,4159,4161,4164,4167,4170,4173,4176,4179],{"className":4160},[1954],[1840,4162],{"className":4163,"style":2739},[1958],[1840,4165,1869],{"className":4166,"style":1968},[1963,1967],[1840,4168,1877],{"className":4169},[2023],[1840,4171,3802],{"className":4172},[1963,1967],[1840,4174],{"className":4175,"style":2084},[1919],[1840,4177,3580],{"className":4178},[2088],[1840,4180],{"className":4181,"style":2084},[1919],[1840,4183,4185,4188,4191,4194,4197,4200],{"className":4184},[1954],[1840,4186],{"className":4187,"style":2739},[1958],[1840,4189,1891],{"className":4190,"style":2075},[1963,1967],[1840,4192,1897],{"className":4193},[2079],[1840,4195],{"className":4196,"style":2084},[1919],[1840,4198,1900],{"className":4199},[2088],[1840,4201],{"className":4202,"style":2084},[1919],[1840,4204,4206,4210,4386],{"className":4205},[1954],[1840,4207],{"className":4208,"style":4209},[1958],"height:2.209em;vertical-align:-0.7693em;",[1840,4211,4213,4216,4383],{"className":4212},[1963],[1840,4214],{"className":4215},[2023,2304],[1840,4217,4219],{"className":4218},[2227],[1840,4220,4222,4374],{"className":4221},[1976,1977],[1840,4223,4225,4371],{"className":4224},[1981],[1840,4226,4229,4254,4262],{"className":4227,"style":4228},[1985],"height:1.4397em;",[1840,4230,4231,4234],{"style":2320},[1840,4232],{"className":4233,"style":2324},[1993],[1840,4235,4237,4240,4244,4248,4251],{"className":4236},[1963],[1840,4238,4003],{"className":4239},[1963,1967],[1840,4241],{"className":4242,"style":4243},[1919],"margin-right:0.2222em;",[1840,4245,4129],{"className":4246},[4247],"mbin",[1840,4249],{"className":4250,"style":4243},[1919],[1840,4252,2233],{"className":4253},[1963,1967],[1840,4255,4256,4259],{"style":2333},[1840,4257],{"className":4258,"style":2324},[1993],[1840,4260],{"className":4261,"style":2341},[2340],[1840,4263,4265,4268],{"style":4264},"top:-3.6897em;",[1840,4266],{"className":4267,"style":2324},[1993],[1840,4269,4271,4274,4277,4280,4283,4328,4331],{"className":4270},[1963],[1840,4272,3988],{"className":4273},[1963,1967],[1840,4275],{"className":4276,"style":4243},[1919],[1840,4278,4129],{"className":4279},[4247],[1840,4281],{"className":4282,"style":4243},[1919],[1840,4284,4286,4291],{"className":4285},[2375],[1840,4287,2239],{"className":4288,"style":4290},[2375,2420,4289],"small-op","position:relative;top:0em;",[1840,4292,4294],{"className":4293},[1972],[1840,4295,4297,4319],{"className":4296},[1976,1977],[1840,4298,4300,4316],{"className":4299},[1981],[1840,4301,4304],{"className":4302,"style":4303},[1985],"height:0.162em;",[1840,4305,4307,4310],{"style":4306},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1840,4308],{"className":4309,"style":1994},[1993],[1840,4311,4313],{"className":4312},[1998,1999,2000,2001],[1840,4314,2244],{"className":4315},[1963,1967,2001],[1840,4317,2010],{"className":4318},[2009],[1840,4320,4322],{"className":4321},[1981],[1840,4323,4326],{"className":4324,"style":4325},[1985],"height:0.2997em;",[1840,4327],{},[1840,4329],{"className":4330,"style":2159},[1919],[1840,4332,4334,4337],{"className":4333},[1963],[1840,4335,1891],{"className":4336,"style":2075},[1963,1967],[1840,4338,4340],{"className":4339},[1972],[1840,4341,4343,4363],{"className":4342},[1976,1977],[1840,4344,4346,4360],{"className":4345},[1981],[1840,4347,4349],{"className":4348,"style":2043},[1985],[1840,4350,4351,4354],{"style":2512},[1840,4352],{"className":4353,"style":1994},[1993],[1840,4355,4357],{"className":4356},[1998,1999,2000,2001],[1840,4358,2244],{"className":4359},[1963,1967,2001],[1840,4361,2010],{"className":4362},[2009],[1840,4364,4366],{"className":4365},[1981],[1840,4367,4369],{"className":4368,"style":2017},[1985],[1840,4370],{},[1840,4372,2010],{"className":4373},[2009],[1840,4375,4377],{"className":4376},[1981],[1840,4378,4381],{"className":4379,"style":4380},[1985],"height:0.7693em;",[1840,4382],{},[1840,4384],{"className":4385},[2079,2304],[1840,4387,2284],{"className":4388},[1963],[1796,4390,4391,4392,4444,4445,4497,4498,4560],{},"代码比较 ",[1840,4393,4395,4414],{"className":4394},[1847],[1840,4396,4398],{"className":4397},[1851],[1853,4399,4400],{"xmlns":1855},[1858,4401,4402,4411],{},[1861,4403,4404,4406,4408],{},[1867,4405,2233],{},[1874,4407,1900],{},[1927,4409,4410],{},"5",[1943,4412,4413],{"encoding":1945},"n=5",[1840,4415,4417,4435],{"className":4416,"ariaHidden":1916},[1950],[1840,4418,4420,4423,4426,4429,4432],{"className":4419},[1954],[1840,4421],{"className":4422,"style":3352},[1958],[1840,4424,2233],{"className":4425},[1963,1967],[1840,4427],{"className":4428,"style":2084},[1919],[1840,4430,1900],{"className":4431},[2088],[1840,4433],{"className":4434,"style":2084},[1919],[1840,4436,4438,4441],{"className":4437},[1954],[1840,4439],{"className":4440,"style":3538},[1958],[1840,4442,4410],{"className":4443},[1963]," 与 ",[1840,4446,4448,4467],{"className":4447},[1847],[1840,4449,4451],{"className":4450},[1851],[1853,4452,4453],{"xmlns":1855},[1858,4454,4455,4464],{},[1861,4456,4457,4459,4461],{},[1867,4458,2233],{},[1874,4460,1900],{},[1927,4462,4463],{},"50",[1943,4465,4466],{"encoding":1945},"n=50",[1840,4468,4470,4488],{"className":4469,"ariaHidden":1916},[1950],[1840,4471,4473,4476,4479,4482,4485],{"className":4472},[1954],[1840,4474],{"className":4475,"style":3352},[1958],[1840,4477,2233],{"className":4478},[1963,1967],[1840,4480],{"className":4481,"style":2084},[1919],[1840,4483,1900],{"className":4484},[2088],[1840,4486],{"className":4487,"style":2084},[1919],[1840,4489,4491,4494],{"className":4490},[1954],[1840,4492],{"className":4493,"style":3538},[1958],[1840,4495,4463],{"className":4496},[1963]," 的重复抽样 MSE。先验均值 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步",[1840,5025,5027],{"className":5026},[1843],[1840,5028,5030,5098],{"className":5029},[1847],[1840,5031,5033],{"className":5032},[1851],[1853,5034,5035],{"xmlns":1855,"display":1856},[1858,5036,5037,5095],{},[1861,5038,5039,5055,5057,5059,5061,5071,5073,5075,5077,5079,5091,5093],{},[4671,5040,5041,5043],{},[1867,5042,1872],{},[1861,5044,5045,5047,5049,5051,5053],{},[1874,5046,1888],{"stretchy":1876},[1867,5048,4624],{},[1874,5050,4129],{},[1927,5052,1929],{},[1874,5054,1894],{"stretchy":1876},[1874,5056,1900],{},[1867,5058,3174],{},[1874,5060,2708],{},[3178,5062,5063,5069],{},[1861,5064,5065,5067],{},[1867,5066,3184],{},[1874,5068,2708],{},[1867,5070,1872],{},[1867,5072,4663],{},[1874,5074,1888],{"stretchy":1876},[1867,5076,1872],{},[1874,5078,3580],{},[4671,5080,5081,5083],{},[1867,5082,1872],{},[1861,5084,5085,5087,5089],{},[1874,5086,1888],{"stretchy":1876},[1867,5088,4624],{},[1874,5090,1894],{"stretchy":1876},[1874,5092,1894],{"stretchy":1876},[1867,5094,2284],{"mathvariant":2283},[1943,5096,5097],{"encoding":1945},"\\theta^{(t+1)}\n=\\arg\\max_\\theta Q(\\theta\\mid\\theta^{(t)}).",[1840,5099,5101,5160,5241],{"className":5100,"ariaHidden":1916},[1950],[1840,5102,5104,5107,5151,5154,5157],{"className":5103},[1954],[1840,5105],{"className":5106,"style":4799},[1958],[1840,5108,5110,5113],{"className":5109},[1963],[1840,5111,1872],{"className":5112,"style":2005},[1963,1967],[1840,5114,5116],{"className":5115},[1972],[1840,5117,5119],{"className":5118},[1976],[1840,5120,5122],{"className":5121},[1981],[1840,5123,5125],{"className":5124,"style":4799},[1985],[1840,5126,5127,5130],{"style":4802},[1840,5128],{"className":5129,"style":1994},[1993],[1840,5131,5133],{"className":5132},[1998,1999,2000,2001],[1840,5134,5136,5139,5142,5145,5148],{"className":5135},[1963,2001],[1840,5137,1888],{"className":5138},[2023,2001],[1840,5140,4624],{"className":5141},[1963,1967,2001],[1840,5143,4129],{"className":5144},[4247,2001],[1840,5146,1929],{"className":5147},[1963,2001],[1840,5149,1894],{"className":5150},[2079,2001],[1840,5152],{"className":5153,"style":2084},[1919],[1840,5155,1900],{"className":5156},[2088],[1840,5158],{"className":5159,"style":2084},[1919],[1840,5161,5163,5167,5172,5175,5220,5223,5226,5229,5232,5235,5238],{"className":5162},[1954],[1840,5164],{"className":5165,"style":5166},[1958],"height:1.5021em;vertical-align:-0.7521em;",[1840,5168,3334,5170],{"className":5169},[2375],[1840,5171,1882],{"style":3040},[1840,5173],{"className":5174,"style":2159},[1919],[1840,5176,5178],{"className":5177},[2375,2376],[1840,5179,5181,5211],{"className":5180},[1976,1977],[1840,5182,5184,5208],{"className":5183},[1981],[1840,5185,5187,5198],{"className":5186,"style":3352},[1985],[1840,5188,5189,5192],{"style":3355},[1840,5190],{"className":5191,"style":2324},[1993],[1840,5193,5195],{"className":5194},[1998,1999,2000,2001],[1840,5196,1872],{"className":5197,"style":2005},[1963,1967,2001],[1840,5199,5200,5203],{"style":3239},[1840,5201],{"className":5202,"style":2324},[1993],[1840,5204,5205],{},[1840,5206,3184],{"className":5207},[2375],[1840,5209,2010],{"className":5210},[2009],[1840,5212,5214],{"className":5213},[1981],[1840,5215,5218],{"className":5216,"style":5217},[1985],"height:0.7521em;",[1840,5219],{},[1840,5221],{"className":5222,"style":2159},[1919],[1840,5224,4663],{"className":5225},[1963,1967],[1840,5227,1888],{"className":5228},[2023],[1840,5230,1872],{"className":5231,"style":2005},[1963,1967],[1840,5233],{"className":5234,"style":2084},[1919],[1840,5236,3580],{"className":5237},[2088],[1840,5239],{"className":5240,"style":2084},[1919],[1840,5242,5244,5247,5285,5288],{"className":5243},[1954],[1840,5245],{"className":5246,"style":4780},[1958],[1840,5248,5250,5253],{"className":5249},[1963],[1840,5251,1872],{"className":5252,"style":2005},[1963,1967],[1840,5254,5256],{"className":5255},[1972],[1840,5257,5259],{"className":5258},[1976],[1840,5260,5262],{"className":5261},[1981],[1840,5263,5265],{"className":5264,"style":4799},[1985],[1840,5266,5267,5270],{"style":4802},[1840,5268],{"className":5269,"style":1994},[1993],[1840,5271,5273],{"className":5272},[1998,1999,2000,2001],[1840,5274,5276,5279,5282],{"className":5275},[1963,2001],[1840,5277,1888],{"className":5278},[2023,2001],[1840,5280,4624],{"className":5281},[1963,1967,2001],[1840,5283,1894],{"className":5284},[2079,2001],[1840,5286,1894],{"className":5287},[2079],[1840,5289,2284],{"className":5290},[1963],[1796,5292,5293],{},"EM 保证观测数据似然不下降，但：",[5295,5296,5297,5300,5303,5306],"ul",{},[1817,5298,5299],{},"可能收敛到局部极值或鞍点；",[1817,5301,5302],{},"收敛可很慢；",[1817,5304,5305],{},"混合成分标签不可识别；",[1817,5307,5308],{},"标准误不能从最后一次 M 步的普通 Hessian 直接猜测。",[1796,5310,5311],{},"应使用多个起点、监控观测对数似然并检查退化解。",[1807,5313,5315],{"id":5314},"_6-方法怎样选择","6. 方法怎样选择",[3707,5317,5318,5331],{},[3710,5319,5320],{},[3713,5321,5322,5325,5328],{},[3716,5323,5324],{},"场景",[3716,5326,5327],{},"起点",[3716,5329,5330],{},"关键审查",[3723,5332,5333,5344,5355,5366,5377],{},[3713,5334,5335,5338,5341],{},[3728,5336,5337],{},"有简单理论矩",[3728,5339,5340],{},"矩估计",[3728,5342,5343],{},"矩是否存在、效率",[3713,5345,5346,5349,5352],{},[3728,5347,5348],{},"完整概率模型可信",[3728,5350,5351],{},"MLE",[3728,5353,5354],{},"支持集、边界、模型错误",[3713,5356,5357,5360,5363],{},[3728,5358,5359],{},"有可辩护先验信息",[3728,5361,5362],{},"Bayes",[3728,5364,5365],{},"先验敏感性、计算诊断",[3713,5367,5368,5371,5374],{},[3728,5369,5370],{},"潜类别\u002F缺失数据",[3728,5372,5373],{},"EM 或 MCMC",[3728,5375,5376],{},"可识别性、局部极值",[3713,5378,5379,5382,5385],{},[3728,5380,5381],{},"只信部分矩条件",[3728,5383,5384],{},"GMM",[3728,5386,5387],{},"工具\u002F矩有效性、权重矩阵",[1807,5389,5391],{"id":5390},"_7-诊断清单","7. 诊断清单",[5295,5393,5394,5397,5400,5403,5406,5409,5412],{},[1817,5395,5396],{},"参数空间和数据支持是否匹配？",[1817,5398,5399],{},"似然是否有界、极值是否唯一？",[1817,5401,5402],{},"优化是否对起点和尺度敏感？",[1817,5404,5405],{},"MLE 的正则条件是否成立？",[1817,5407,5408],{},"先验在数据尺度上意味着什么？",[1817,5410,5411],{},"后验计算是否收敛，有效样本量如何？",[1817,5413,5414],{},"EM 的观测似然是否单调，是否尝试多个起点？",[1807,5416,5417],{"id":5417},"课堂任务",[1796,5419,5420,5421,5579],{},"对 ",[1840,5422,5424,5474],{"className":5423},[1847],[1840,5425,5427],{"className":5426},[1851],[1853,5428,5429],{"xmlns":1855},[1858,5430,5431,5471],{},[1861,5432,5433,5439,5441,5443,5445,5447,5449,5451,5454,5456,5458,5460,5462,5465,5467,5469],{},[1864,5434,5435,5437],{},[1867,5436,1891],{},[1867,5438,2244],{},[1874,5440,3780],{},[1867,5442,1869],{},[1867,5444,2637],{},[1867,5446,1796],{},[1867,5448,3786],{},[1867,5450,2233],{},[1867,5452,5453],{},"e",[1867,5455,2233],{},[1867,5457,4624],{},[1867,5459,2244],{},[1867,5461,3988],{},[1867,5463,5464],{},"l",[1874,5466,1888],{"stretchy":1876},[1867,5468,3802],{},[1874,5470,1894],{"stretchy":1876},[1943,5472,5473],{"encoding":1945},"X_i\\sim Exponential(\\lambda)",[1840,5475,5477,5532],{"className":5476,"ariaHidden":1916},[1950],[1840,5478,5480,5483,5523,5526,5529],{"className":5479},[1954],[1840,5481],{"className":5482,"style":3817},[1958],[1840,5484,5486,5489],{"className":5485},[1963],[1840,5487,1891],{"className":5488,"style":2075},[1963,1967],[1840,5490,5492],{"className":5491},[1972],[1840,5493,5495,5515],{"className":5494},[1976,1977],[1840,5496,5498,5512],{"className":5497},[1981],[1840,5499,5501],{"className":5500,"style":2043},[1985],[1840,5502,5503,5506],{"style":2512},[1840,5504],{"className":5505,"style":1994},[1993],[1840,5507,5509],{"className":5508},[1998,1999,2000,2001],[1840,5510,2244],{"className":5511},[1963,1967,2001],[1840,5513,2010],{"className":5514},[2009],[1840,5516,5518],{"className":5517},[1981],[1840,5519,5521],{"className":5520,"style":2017},[1985],[1840,5522],{},[1840,5524],{"className":5525,"style":2084},[1919],[1840,5527,3780],{"className":5528},[2088],[1840,5530],{"className":5531,"style":2084},[1919],[1840,5533,5535,5538,5541,5544,5547,5550,5553,5556,5559,5562,5566,5570,5573,5576],{"className":5534},[1954],[1840,5536],{"className":5537,"style":2739},[1958],[1840,5539,1869],{"className":5540,"style":1968},[1963,1967],[1840,5542,2637],{"className":5543},[1963,1967],[1840,5545,1796],{"className":5546},[1963,1967],[1840,5548,3786],{"className":5549},[1963,1967],[1840,5551,2233],{"className":5552},[1963,1967],[1840,5554,5453],{"className":5555},[1963,1967],[1840,5557,2233],{"className":5558},[1963,1967],[1840,5560,4624],{"className":5561},[1963,1967],[1840,5563,5565],{"className":5564},[1963,1967],"ia",[1840,5567,5464],{"className":5568,"style":5569},[1963,1967],"margin-right:0.0197em;",[1840,5571,1888],{"className":5572},[2023],[1840,5574,3802],{"className":5575},[1963,1967],[1840,5577,1894],{"className":5578},[2079],"（rate 参数化）：",[1814,5581,5582,5585,5588,5591,5594],{},[1817,5583,5584],{},"用一阶矩构造矩估计；",[1817,5586,5587],{},"推导 MLE；",[1817,5589,5590],{},"选择 Gamma 先验并写出后验；",[1817,5592,5593],{},"比较后验均值、MAP 与 MLE；",[1817,5595,5596],{},"说明若软件使用 scale 参数会怎样造成错误。",[1807,5598,5599],{"id":5599},"核心阅读",[5295,5601,5602,5610,5622],{},[1817,5603,5604,5605,5609],{},"Casella & Berger, ",[5606,5607,5608],"em",{},"Statistical Inference","，估计方法章节。",[1817,5611,5612,5613,5621],{},"Gelman et al., ",[3988,5614,5618],{"href":5615,"rel":5616},"https:\u002F\u002Fwww.stat.columbia.edu\u002F~gelman\u002Fbook\u002F",[5617],"nofollow",[5606,5619,5620],{},"Bayesian Data Analysis","。",[1817,5623,5624,5625,5621],{},"Dempster, Laird & Rubin (1977), ",[3988,5626,5629],{"href":5627,"rel":5628},"https:\u002F\u002Fdoi.org\u002F10.1111\u002Fj.2517-6161.1977.tb01600.x",[5617],"“Maximum Likelihood from Incomplete Data via the EM Algorithm”",[1796,5631,5632,5633,5637,5638,5621],{},"上一章：",[3988,5634,5636],{"href":5635},"..\u002F03-point-estimation\u002F","点估计理论","｜下一章：",[3988,5639,5641],{"href":5640},"..\u002F05-hypothesis\u002F","假设检验原理",{"title":10,"searchDepth":5643,"depth":5643,"links":5644},2,[5645,5646,5647,5648,5649,5650,5655,5656,5657,5658],{"id":1809,"depth":5643,"text":1809},{"id":1834,"depth":5643,"text":1835},{"id":2608,"depth":5643,"text":2609},{"id":3554,"depth":5643,"text":3555},{"id":3755,"depth":5643,"text":3756},{"id":4573,"depth":5643,"text":4574,"children":5651},[5652,5654],{"id":4644,"depth":5653,"text":4645},3,{"id":5022,"depth":5653,"text":5023},{"id":5314,"depth":5643,"text":5315},{"id":5390,"depth":5643,"text":5391},{"id":5417,"depth":5643,"text":5417},{"id":5599,"depth":5643,"text":5599},"比较矩估计、极大似然、贝叶斯估计和 EM 算法的构造逻辑、计算与边界。","md",{"sidebar":5662},{"order":5663},10,true,{"title":1704,"description":5659},"Ftesak_XRlPl0ExEtCigugvPJn5fh7lzCDLZBwG7RxQ",[5668,5670],{"title":1698,"path":1699,"stem":1700,"description":5669,"children":-1},"用偏差、方差、MSE、一致性、充分性、效率与稳健性评价估计量。",{"title":1710,"path":1711,"stem":1712,"description":5671,"children":-1},"从错误概率、p 值与功效出发，理解 Neyman–Pearson、似然比、可选停止和多重检验。",1785754757288]