基于DIRICHLET过程的非参数贝叶斯分析

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1、西南交通大学硕士学位论文基于Dirichlet过程的非参数贝叶斯分析姓名：姚宗静申请学位级别：硕士专业：概率论与数理统计指导教师：赵联文20070301西南交通大学硕士研究生学位论文第1I页的先验分布类，并证明它是满足上述两点要求的。(2)讨论了简单Dirichlet过程的性质，并给出了在可测剖分下它的有限阶原点距，方差，协方差等数字特征。(3)讨论了它的支撵问题，证明它的支撑是足够大的。(4)求出了在该先验类下其后验的具体表达形式。关键词：简单Dirichlet过程；非参数；概率测度：先验类；

2、后验分布西南交通大学硕士研究生学位论文第1II页AbstractTheBayesianapproachtostatisticalproblems，thoughfruitfulinmanyways，hasbeenratherunsuccessfulintreatingnonparametricproblems．ThisisdueprimarilytothedifficultyinfindingworkablepriordistributionsOiltheparameterspace．whichi

3、nnonparametricproblemsistakentobeasetofprobabilitydistributionsonagivensamplespace．BasedonthepaperofFergnsonin1973，therearetwodesirablepropertiesofapriordistributionfornonparametrieproblems：(1)Thesupportofthepriordistributionshouldbelarge-withrespect

4、tosomesuitabletopologyonthespaceofprobabihtydistributionsonthesamplespace．Thisvanassurethefeasibilityanduniversalityoftheprior，SOwecallfindthebestmodelforthedistribution．(2)Poeteriordistributionsgivenasampieofobservationsfromthetrueprobabilityshouldb

5、emanageableanalytically．ItrequiresthePosteriordis-tributionshavethesameformsasthepriors，ortheyareconjugateclasses，ortheycaneasilybecomputed．Thesepropertiesareantagonisticinthesensethatonemaybeobtainedattheexpenseoftheother．Weusuallybroadaclassofprior

6、distributionsintheseuseof(1)，forwhich(2)isrealizedbygivenintheseilseofconjugateclass．Refertothepapersinthepastfewdecades，themethodweusedmostistofollowtheideaofFergnsonin1973．ThepaperofJayaramSethuramanin1994isthebestexampleofthisidea，hegivesasimplean

7、dnewconstructivedefinitionofDirichletmeasuresremovingtherestrictionthatthebasicspaceshouldbem．Inmypaper，aumfyingframeworkforBayesiananalysisinnon-parametricsettingisproposed．Tothisaim，ageneralclassofnonparametric堕塑壅塑壅堂塑主堡窒竺兰堡堡塞蒸翌夏priordistributionson

8、allarbitrarysamplespaceisintroduced．Thegeneralstructureofposteriorandpredictivedistributionsaredeveloped．Thispaperdoestheworkasfollowing：(1)GiventhedefinitionofsimpleDirichletprocess．provedthatitisthepriordistributionsinnonparametricprobleins．(2)Disc