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ID:49472826
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页数:50页
时间:2020-02-07
《Bayesian Statistics and Inference III贝叶斯统计.ppt》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库。
1、BayesianStatisticsandInferenceIIIDrTeng,JHarbinInstituteofTechnologyOutlinesContrastbetweenMaximumLikelihoodapproachandBayesianapproachExamplesofBayesiandecisionmakingandvalueofinformationEstimationofunknownparametersinstatisticalmodels(Bayesianandnon-Bayesian)Supposewepositapro
2、babilitydistributiontomodeldata.Howdoweestimateitsunknownparameters?Example:assumedatafollowregressionmodel.Wheredotheestimatesoftheregressioncoefficientscomefrom?Classicalstatistics:maximumlikelihoodestimation.Bayesianstatistics:Bayesrule.EstimatingpercentageofDukieswhoplantoge
3、tadvanceddegreeSupposewewanttoestimatethepercentageofDukestudentswhoplantogetanadvanceddegree(MBA,JD,MD,PhD,etc.).Callthispercentagep.Wesample20peopleatrandom,and8ofthemsaytheyplantogetanadvanceddegree.Whatshouldbeourestimateofp?EstimatingtheaverageIQofDukeprofessorsLetµbethepo
4、pulationaverageIQofDukeprofs.Supposewerandomlysample25DukeprofsandrecordtheirIQs.Whatshouldbeourestimateofµ?Maximumlikelihoodestimation:AprincipledapproachtoestimationUsuallywecanusesubject-matterknowledgetospecifyadistributionforthedata.But,wedon’tknowtheparametersofthatdistri
5、bution.1)Numberoutof20whowantadvanceddegree:binomialdistribution.2)Profs’IQs:normaldistribution.MaximumlikelihoodestimationWeneedtoestimatetheparametersofthedistribution.Whydowecare?A)Sowecanmakeprobabilitystatementsaboutfutureevents.B)Theparametersthemselvesmaybeimpor
6、tant.MaximumlikelihoodestimationThemaximumlikelihoodestimateoftheunknownparameteristhevalueforwhichthedataweremostlikelytohaveoccurred.Let’sseehowthisworksintheexamples.AdvanceddegreeexampleLetYbetherandomvariableforthenumberofpeopleoutof20thatplantogetanadvanceddegree.Yhasabino
7、mialdistributionwithn=20,andunknownprobabilityp.Inthedata,Y=8.Ifweknewp,thevalueoftheprobabilitydistributionfunctionatY=8wouldbe:MaximumlikelihoodLabelthefunctionL(p).L(p)iscalledthelikelihoodfunctionforp.ThemaximumlikelihoodestimateofpisthevalueofpthatmaximizesL(p).Thisisareaso
8、nableestimatebecauseitisthevalueofpforwhichtheo
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