资源描述：
《贝叶斯方法在精算模型中的应用》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
1、无论在哪个方面，对模型的研究都是重屮Z重。本文主要介绍了线性信度模型、修匀模型、MCMC模型和时间序列回归模型；其中在线性信度模型中推导了Buhlmann模型和Buhlmann—Straub模型以及它们的经验贝叶斯估计，说明了应用范围和计算过程；在修匀模型中介绍了Kimeldorf・Jones方法和Dirichlet方法，并得到了修匀估计量的一般形式；在MCMC模型屮介绍了其原理以及如何应用；在时间序列回归模型中介绍了AR(p)模型和MA(q濮型，并推导了参数估计和预测分布的表达形式。最后，对贝叶斯方法在索赔次数
2、和保费中的应用给出了四个算例。关键词：贝叶斯方法；先验分布；信度估计；时间序列冋归模型TheapplicationofBayesianmethodinactuarialmodelAbstractWithcontinuousdevelopmentofthetheoiyofprobabilityandstatistics,theBayesianmethodshowsitsuniqueadvantagesgradually,andformsaveryinfluentialschoolofthought,anditsin
3、fluencecontinuestoexpand,eveneveryfieldofhumanstudiesexistsacertainlevelofbayesiananalysis.TheresearchandapplicationoftheBayesianmethodinactuarialmainlydividedintothefollowingthreeaspects:experiencerateestimation,lossreservesandcompoundlossmodels,updatingdata
4、andlifetable.Inthispaper,wesummarizedtheoriginofthedevelopmentoftheBayesianmethodandthepresentstatusofreseaivhbothathomeandabroad,expoundedthereasoningthinkingoftheBayesianmethodandthestepsofparameterestimation,detailedthebayesianreliabilityestimation,derived
5、severalimportantconclusions,clarifiedtherelationshipbetweenthebayespremiumandsomeimportantestimator,andfocusedonthemethodofdeteiTninationandselectionofpriordistributionandseveralconclusionsinconjugatepriordistribution.Nomatterinwhichaspect,thestudyofmodelisto
6、ppriority.Thisarticlemainlyintroducedthelinearreliabilitymodeljhegraduationmodel,theMCMCmodelandthetimeseriesregressionmodel.TheBuhlmannmodel,theBuhlmann-Straubmodelandtheirempiricalbayesianestimationwerededucedinthelinearreliabilitymodel,andtheirappliedrange
7、andcomputationalprocesswereillustrated.TheKimeldorf-JonesmethodandtheDirichletmethodwereintroducedinthegraduationmodel,andthegeneralformofestimatorofgraduationwereobtained.ThetheoryofMCMCmodelandthestepsofitsapplicationwereintroduced.TheAR(p)modelandtheMA(q)m
8、odelwereintroducedinthetimeseriesregressionmodel,andtheexpressionsofparameterestimationandpredictivedistributionwerededuced.Finally.theapplicationoftheBayesianmethodtoclaimfrequencyandpre
