貝葉斯統(tǒng)計(jì)教學(xué)大綱

《貝葉斯統(tǒng)計(jì)》教學(xué)大綱“BayesianStatistics”CourseOutline課程編號(hào)：152053A課程類型：專業(yè)選修課總學(xué)時(shí)：48授課學(xué)時(shí)：48實(shí)驗(yàn)（上機(jī)）學(xué)時(shí)：0學(xué)分：3合用對象：金融學(xué)（金融經(jīng)濟(jì)）先修課程：數(shù)學(xué)分析、概率論與數(shù)理統(tǒng)計(jì)、計(jì)量經(jīng)濟(jì)學(xué)CourseCode：152053ACourseType：DisciplineElectiveTotalHours：48Lecture：48Experiment(Computer)：0Credit：3ApplicableMajor：Finance（FinanceandEconomicsExperimentClass）Prerequisite：MathematicalAnalysis,ProbabilityTheoryandStatistics,Econometrics一、課程的教學(xué)目的本課程旨在向?qū)W生介紹貝葉斯統(tǒng)計(jì)理論、貝葉斯統(tǒng)計(jì)辦法及其在實(shí)證研究中的應(yīng)用。貝葉斯統(tǒng)計(jì)理論與傳統(tǒng)統(tǒng)計(jì)理論遵照著不同的基本假設(shè)，為我們解決數(shù)據(jù)信息提供新的角度和解讀思路，并在解決某些復(fù)雜模型上（如，預(yù)計(jì)動(dòng)態(tài)隨機(jī)普通均衡模型、帶時(shí)變參數(shù)的狀態(tài)空間模型等）相比傳統(tǒng)辦法含有相對優(yōu)勢。本課程規(guī)定學(xué)生在選課前含有基本的微積分、概率統(tǒng)計(jì)以及計(jì)量經(jīng)濟(jì)學(xué)知識(shí)。以此為起點(diǎn)，我們將重要就貝葉斯統(tǒng)計(jì)理論知識(shí)、統(tǒng)計(jì)模型的應(yīng)用以及基于計(jì)算機(jī)編程的實(shí)證能力三方面對學(xué)生進(jìn)行訓(xùn)練。通過對本課程的學(xué)習(xí)，學(xué)生應(yīng)理解貝葉斯框架的基本思想，掌握基本的貝葉斯理論辦法及其重要應(yīng)用，并掌握實(shí)證研究中慣用的貝葉斯數(shù)值抽樣辦法以及有關(guān)的計(jì)算機(jī)編程技能。特別地，學(xué)生應(yīng)能明確理解貝葉斯統(tǒng)計(jì)辦法與傳統(tǒng)統(tǒng)計(jì)辦法在思想和應(yīng)用上的區(qū)別以及各自的優(yōu)缺點(diǎn)，方便能在實(shí)際應(yīng)用中合理選擇統(tǒng)計(jì)分析工具。ThiscourseintroducesthebasicconceptsofBayesianstatisticsandtheuseofBayesianeconometricmethodsinempiricalstudy.Bayesianstatisticshasdifferentfundamentalassumptionsfromtheclassical(frequentist)framework,providinguswithanalternativewayinanalyzingandinterpretingdatainformation.Bayesianmethodsalsohaverelativeadvantages,andthusarewidelyused,indealingwithcertaincomplicatedmodels(forexample,theestimationofDynamicStochasticGeneralEquilibriummodel,statespacemodelswithtime-varyingparameters,etc.).Studentsshouldhavehadbasictrainingsoncalculus,probabilitytheoryandstatistics,andpreferablyeconometricspriortothiscourse.ThemajortrainingsofferedinthiscoursefocusonBayesiantheories,Bayesianstatisticalmodelswithapplicationsandcomputationalskillsrequiredforempiricalanalysis.Afterthecourse,studentsshoulddeveloptheirunderstandingonthephilosophyofBayesianframework,understandbasicBayesiantheories,Bayesianestimationmethodsandtheirapplications,andmasterthecomputerskillsforthepracticaluseofBayesianmethods.Specifically,studentsshouldunderstandthedifferencesbetweentheBayesianviewpointandtheclassicalfrequentistperspectiveinordertobeabletochooseappropriateanalyzingtoolsinempiricaluse.二、教學(xué)基本規(guī)定貝葉斯統(tǒng)計(jì)學(xué)和計(jì)量辦法在近年得到越來越廣泛的關(guān)注和應(yīng)用，重要得益于計(jì)算機(jī)技術(shù)的發(fā)展使得貝葉斯數(shù)值抽樣辦法在實(shí)際應(yīng)用中得以實(shí)現(xiàn)。因此，除了對貝葉斯有關(guān)理論的講授，計(jì)算機(jī)數(shù)值辦法的介紹與有關(guān)實(shí)踐也是同等重要的。統(tǒng)計(jì)理論的部分，本課程重要涵蓋貝葉斯定理以及貝葉斯辦法的基本數(shù)據(jù)分析框架，以及運(yùn)用貝葉斯辦法進(jìn)行回歸模型的預(yù)計(jì)、預(yù)測和模型比較的基本辦法。數(shù)值辦法部分，重要介紹MarkovChainMonteCarlo后驗(yàn)分布抽樣辦法（Gibbs抽樣法和Methopolis-Hastings抽樣法），以及邊沿似然函數(shù)和貝葉斯因子的預(yù)計(jì)辦法等。這兩部分的內(nèi)容應(yīng)緊密結(jié)合并輔以實(shí)例分析，以課堂講授結(jié)累計(jì)算機(jī)演示的方式進(jìn)行教學(xué)。另外，貝葉斯辦法與傳統(tǒng)統(tǒng)計(jì)辦法的對比也應(yīng)貫穿課程各章節(jié)，以協(xié)助學(xué)生理解兩種辦法的優(yōu)缺點(diǎn)及合用范疇，為實(shí)際應(yīng)用提供指導(dǎo)。對應(yīng)課堂內(nèi)容，課后作業(yè)也應(yīng)強(qiáng)調(diào)理論和實(shí)踐的結(jié)合，編程練習(xí)應(yīng)占重要比例。教師應(yīng)提供必要的編程軟件使用指導(dǎo)，并指導(dǎo)學(xué)生根據(jù)提供的范例練習(xí)運(yùn)用貝葉斯辦法進(jìn)行數(shù)據(jù)分析。課程考核方式及其權(quán)重以下：出勤10%作業(yè)20%期末閉卷考試30%課程論文30%課程論文宣講10%Thankstothedevelopmentofcomputertechnology,BayesianstatisticsandeconometricshasbecomemorepopularasBayesiancomputationalmethodshavebecomepractical.ComputationalmethodsareasimportantastheoriestoBayesianstatistics,soastothiscourse.Inthetheoreticalstatisticspart,thiscourseinvolvelecturesonBayesTheorem,thegeneralBayesiananalysisframework,andthegeneralapproachestoestimatemodels,developpredictionsandcomparemodelsintheBayesianway.Intermsofcomputationalmethods,wewillmainlyintroducetheMCMCposteriorsampling(theGibbsSamplingandtheMetropolis-HastingAlgorithm),andtheapproximationtechniqueformarginallikelihoodandtheBayesfactor.Thetwopartsshouldintroducedalongwitheachother.Empiricalandcomputerillustrationsarealsonecessaryforstudentstounderstandtheapproach.Lastbutnottheleast,instructorshouldhavetheBayesianframeworkcomparedwiththeClassicalfrequentistframeworkinallaspectswhenappropriateinordertoillustratetheadvantages/disadvantagesofthetwoframeworks,providingstudentswithempiricalinstructions.Homeworkassignmentsshouldbecomposedofderivationsandcomputerexercises.Propersoftwareinstructionsandexamplesshouldbeprovidedtofacilitatestudents’practiceonBayesiananalysistechniques.Thegradingweightsareasfollows:Attendancy10%HomeworkAssignments20%FinalExam(ClosedBook)30%TermPaper30%TermPaperPresentations10%三、各教學(xué)環(huán)節(jié)學(xué)時(shí)分派序號(hào)章節(jié)內(nèi)容授課實(shí)驗(yàn)其它累計(jì)1課程介紹及貝葉斯定理CourseOverviewandBayesTheorem20022貝葉斯統(tǒng)計(jì)理論初步ElementsofBayesianInference40043線性回歸模型（假設(shè)共軛先驗(yàn)分布）LinearRegressionModelswithNaturalConjugatePriors60064線性回歸模型（假設(shè)其它先驗(yàn)分布）LinearRegressionModelswithOtherPriors90095非線性回歸模型NonlinearRegression60066潛在變量模型ModelswithLatentVariables60067時(shí)間序列模型TimeSeriesModels60068貝葉斯模型比較與模型平均BayesianModelComparisonsandModelAveraging60069論文宣講TermPaperPresentations3003累計(jì)480048

四、教學(xué)內(nèi)容第一章課程介紹及貝葉斯定理第一節(jié)課程介紹第二節(jié)貝葉斯定理貝葉斯定理貝葉斯定理的簡樸應(yīng)用教學(xué)重點(diǎn)、難點(diǎn)：貝葉斯定理的涵義并通過實(shí)例闡釋。課程考核規(guī)定：掌握貝葉斯定理的涵義，并能運(yùn)用定理對對簡樸的事件作出推論。Chapter1CourseOverviewandBayesTheoremSection1CourseOverviewSection2BayesTheoremBayesTheoremSimpleApplicationsofBayesTheoremKeyandDifficultPoints:thekeyideaofBayesTheorempresentedwithexamples.EvaluationRequirements:masterthekeyideaofBayesTheorem,andmakeinferenceswiththetheoreminsimplescenarios.第二章貝葉斯統(tǒng)計(jì)理論初步第一節(jié)貝葉斯統(tǒng)計(jì)理論的基本要素先驗(yàn)分布與后驗(yàn)分布貝葉斯定理的應(yīng)用貝葉斯統(tǒng)計(jì)與傳統(tǒng)統(tǒng)計(jì)辦法的系統(tǒng)性差別第二節(jié)點(diǎn)預(yù)計(jì)和置信區(qū)間點(diǎn)預(yù)計(jì)最高后驗(yàn)密度區(qū)間第三節(jié)貝葉斯決策理論第四節(jié)模型比較邊際似然函數(shù)預(yù)測密度函數(shù)教學(xué)重點(diǎn)、難點(diǎn)：貝葉斯統(tǒng)計(jì)各要素的互有關(guān)聯(lián)，與傳統(tǒng)統(tǒng)計(jì)辦法的根本區(qū)別。課程考核規(guī)定：掌握貝葉斯統(tǒng)計(jì)體系各要素的定義及互相聯(lián)系，理解貝葉斯統(tǒng)計(jì)體系與傳統(tǒng)統(tǒng)計(jì)學(xué)的根本區(qū)別，理解貝葉斯統(tǒng)計(jì)推斷的常見內(nèi)容。Chapter2ElementsofBayesianInferenceSection1BasicElementsofBayesianStatisticsPriorandPosteriorHowBayesTheoremisusedSystematicDifferencesbetweentheBayesianandFrequentistViewSection2PointEstimationandCredibleSetsPointEstimationHighestPosteriorDensityIntervalSection3BayesianDecisionTheorySection4ModelComparisonMarginalLikelihoodsPredictiveDensitiesKeyandDifficultPoints:therelationshipsbetweenelementsofBayesianStatistics,thefundamentaldifferencesbetweentheBayesianviewandthefrequantistview.EvaluationRequirements:mastertheconceptsoftheelementsofBayesianStatisticsandtherelationshipamongthem,understandthefundamentaldifferencesbetweentheBayesianandfrequentistview,andunderstandthecommoncomponentsofBayesianinferences.第三章線性回歸模型（假設(shè)共軛分布）第一節(jié)后驗(yàn)分布的推導(dǎo)用矩陣表達(dá)的線性回歸模型似然函數(shù)共軛先驗(yàn)分布后驗(yàn)分布第二節(jié)預(yù)測第三節(jié)貝葉斯數(shù)值計(jì)算辦法：蒙特卡羅模擬積分第三節(jié)實(shí)證范例教學(xué)重點(diǎn)、難點(diǎn)：后驗(yàn)分布的推導(dǎo)與應(yīng)用，蒙特卡羅模擬積分。課程考核規(guī)定：理解共軛先驗(yàn)分布假設(shè)下的后驗(yàn)分布的推導(dǎo)，掌握運(yùn)用后驗(yàn)分布進(jìn)行實(shí)證分析，掌握蒙特卡羅模擬積分辦法。Chapter3LinearRegressionModelswithNaturalConjugatePriorsSection1DerivationofthePosteriorTheLinearRegressionModelinMatrixNotationTheLikelihoodFunctionTheNaturalConjugatePriorThePosteriorSection2PredictionSection3BayesianComputationalMethods:MonteCarloIntegrationSection4EmpiricalIllustrationsKeyandDifficultPoints:thederivationoftheposterioranditsapplications,MonteCarloIntegration.EvaluationRequirements:understandthederivationoftheposterior,analyzerealdatabasedontheposterior,masterthemethodologyofMonteCarlointegration.第四章線性回歸模型（假設(shè)其它先驗(yàn)分布）第一節(jié)獨(dú)立正態(tài)－伽瑪先驗(yàn)分布獨(dú)立正態(tài)－伽瑪先驗(yàn)分布后驗(yàn)分布第二節(jié)貝葉斯數(shù)值計(jì)算辦法：后驗(yàn)分布Gibbs隨機(jī)抽樣法Gibbs隨機(jī)抽樣法馬爾可夫鏈蒙特卡羅收斂鑒定第三節(jié)帶限制的線性回歸模型后驗(yàn)分布貝葉斯數(shù)值計(jì)算辦法：重要性隨機(jī)抽樣法第四節(jié)實(shí)證范例教學(xué)重點(diǎn)、難點(diǎn)：Gibbs隨機(jī)抽樣法，重要性隨機(jī)抽樣法。課程考核規(guī)定：掌握Gibbs隨機(jī)抽樣法和重要性隨機(jī)抽樣法，理解如何根據(jù)實(shí)際狀況對抽樣辦法做出選擇。Chapter4LinearRegressionModelswithOtherPriorsSection1TheIndependentNormal-GammaPriorTheIndependentNormal-GammaPriorThePosteriorSection2BayesianComputationalMethods:GibbsSamplingGibbsSamplingMCMCConvergenceDiagnosticsSection3LinearRegressionModelswithRestrictionsThePosteriorBayesianComputationalMethods:ImportanceSamplingSection4EmpiricalIllustrationsKeyandDifficultPoints:Gibbssampling,importancesampling.EvaluationRequirements:masterthemethodologyofGibbssamplingandimportancesampling,understandhowtochooseappropriatemethodologygivendifferentscenarios.第五章非線性回歸模型第一節(jié)非線性回歸模型模型設(shè)定先驗(yàn)分布與后驗(yàn)分布第二節(jié)貝葉斯數(shù)值計(jì)算辦法：Metropolis-Hasting抽樣法普通性環(huán)節(jié)獨(dú)立鏈MH抽樣法隨機(jī)游走鏈MH抽樣法Metropolis-within-Gibbs抽樣法第三節(jié)實(shí)證范例教學(xué)重點(diǎn)、難點(diǎn)：MH抽樣法，Metropolis-within-Gibbs抽樣法。課程考核規(guī)定：理解MH抽樣法的普通環(huán)節(jié)，掌握獨(dú)立鏈與隨機(jī)游走鏈MH抽樣法，理解Metropolis-within-Gibbs抽樣法。Chapter5NonlinearRegressionSection1NonlinearRegressionModelSetupThePriorandThePosteriorSection2BayesianComputationalMethods:Metropolis-HastingAlgorithmTheGeneralAlgorithmTheIndependentChainMHAlgorithmTheRandomWalkChainMHAlgorithmMetropolis-within-GibbsSection3EmpiricalIllustrationsKeyandDifficultPoints:Metropolis-HastingAlgorithm,Metropolis-within-Gibbs.EvaluationRequirements:understandthegeneralalgorithmofMetropolis-Hasting,mastertheindependencechain/randomwalkchainMHalgorithm,understandthemethodologyofMetropolis-within-Gibbs.第六章潛在變量模型第一節(jié)刪截線性回歸模型第二節(jié)Probit模型第三節(jié)Tobit模型第四節(jié)帶混合正態(tài)的模型教學(xué)重點(diǎn)、難點(diǎn)：各模型的特點(diǎn)及相對應(yīng)的數(shù)據(jù)特點(diǎn)，各模型合用的后驗(yàn)分布抽樣辦法。課程考核規(guī)定：理解各模型的特點(diǎn)及相對應(yīng)的數(shù)據(jù)特點(diǎn)，理解合用的后驗(yàn)分布抽樣辦法。Chapter6ModelswithLatentVariablesSection1CensoredLinearModelsSection2ProbitModelsSection3TobitModelsSection4ModelingwithMixturesofNormalsKeyandDifficultPoints:featuresoftheabovemodelsandtheircorrespondingdatasets,posteriorsamplingwiththeabovemodels.EvaluationRequirements:understandthefeaturesoftheabovemodelsandtheircorrespondingdatasets,understandthemethodologyforposteriorsampling.第七章時(shí)間序列模型第一節(jié)線性時(shí)間序列模型常見模型普通性預(yù)計(jì)辦法第二節(jié)狀態(tài)空間模型普通模型設(shè)定Gibbs抽樣法MH抽樣法教學(xué)重點(diǎn)、難點(diǎn)：狀態(tài)空間模型的貝葉斯預(yù)計(jì)法。課程考核規(guī)定：掌握普通時(shí)間序列模型的貝葉斯預(yù)計(jì)辦法，理解狀態(tài)空間模型及其貝葉斯預(yù)計(jì)法。Chapter7TimeSeriesModelsSection1LinearTimeSeriesModelsCommonTimeSeriesModelsGeneralBayesianApproachSection2State-SpaceModelsGeneralModelSetupGibbsSamplingMetropolis-HastingAlgorithmKeyandDifficultPoints:Bayesianestimationalgorithmofstate-spacemodels.EvaluationRequirements:masterthegeneralestimationapproachesforlineartimeseriesmodels,understandthesetupofstate-spacemodelsandtheirBayesianestimationalgorithm.第八章貝葉斯模型比較與模型平均第一節(jié)貝葉斯模型比較貝葉斯因子用Gelfand－Dey辦法預(yù)計(jì)邊際似然函數(shù)用Chib辦法預(yù)計(jì)邊際似然函數(shù)（選講）貝葉斯假設(shè)檢查第二節(jié)貝葉斯模型平均教學(xué)重點(diǎn)、難點(diǎn)：貝葉斯因子的應(yīng)用，邊際似然函數(shù)的預(yù)計(jì)。課程考核規(guī)定：掌握貝葉斯因子的定義及應(yīng)用，理解邊際似然函數(shù)的預(yù)計(jì)辦法,理解模型平均的意義。Chapter8BayesianModelComparisonsandModelAveragingSection1Baye