自然數(shù)集上的Dirichlet過程以及無限正態(tài)混合模型.pdf

1、東南大學(xué)碩士學(xué)位論文自然數(shù)集上的Dirichlet過程以及無限正態(tài)混合模型姓名：王平申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：數(shù)學(xué)；概率論與數(shù)理統(tǒng)計(jì)指導(dǎo)教師：江其保20110115AbstractAsanaturalextensionoffinitemixturemodel，weproposecountablyinfinitecombinationsofGaussiandistributionWeconsiderthecoffvexcombination

2、ofZn％I，riN(pi，蠢)asanewclassofdistributionWeanalyzetheinfiniteGaussianmixturemodelbyBayesanalysisWechooseDirichletprocess，NormaldistributionandinverseGammaasthepriorsofcomponentweights，componentmeanandcomponentvalianc2By#

3、vingthepriorsofparametersinthemodel，wecalculatetheposteriordistributionoftheseparametersinthemodelbyusingBayesmethodTherefore，WecanobtaintheBayes’estimationofparametersinthemodelInthispaperwefirstJyconsiderseveralcommonc

4、haractersofDirichletprocessontheabstractspaceBasedonthesecharacters，wederivesomeimportantpropertiesofDirichletprocessOilthesetofnaturalnumbersThen，weanalyzetheinfiniteGaIISsianmixturemodelbasingonDirichletpr0Ice鼴Ontheset

5、ofnaturalnumbersUsingBayesmethodandtheimportantpropertiesofDirichletprocessonthesetofnaturalnumberstocalculatetheposteriordistributionofparametersintheinfiniteGaussianmixturemodelBasingontheseposteriordistributions，wecan

6、sampleandestimatetheparametersintheinfiniteGaussianmixturemodelFinallyweobtaintheestimationofweightinmodel，theestimationofmeaninmodelandtheestimationofvariancebyexperimentalsimulationWealsocorrectlyjudgethenumberofmixtur