【作者】 刘伟；

【导师】 史宁中；

【作者基本信息】 东北师范大学 ， 概率论与数理统计， 2010， 博士

【摘要】 模型选择是统计分析的重要组成部分,也是大多数科学工作的中心.研究人员收集数据后经常希望能够得到一个较好描述数据特征的模型,以后的分析工作都将在假定这个模型是生成数据的真实模型的基础上进行,为此模型的挑选具有非常重要的意义.许多的统计学者从频率的或贝叶斯的角度考虑了模型的挑选,并开发出大量的方法,本文我们就主要围绕模型选择问题展开讨论.现代医药学研究都需要通过统计分析得到一个科学的结论,这篇文章中我们首先就针对药物毒性研究阶段的两组数据进行分析,考虑使用新的剂量反应函数或模型是否更适合.这两组数据中包含了连续型数据与离散型数据,其中,一组是考虑受试者对药物敏感的模式,另一组是考虑受试者与某种药物间的剂量反应关系.我们使用贝叶斯因子与交叉核实两种方法来处理这两个问题,其中由于贝叶斯因子经常是难以计算的,利用Schwarz所描述的贝叶斯因子与贝叶斯信息准则间的关系,我们便可通过后者来简单的计算贝叶斯因子进行模型选择.由于医药学研究关乎人类的生命,因此选择一个最适合的模型对后续的风险评估工作的开展是极其重要的.本文的另一项主要工作就是对变量选择问题的研究.混合模型由于其特殊的模型结构能有效地反映数据中潜在的异质性,因而得到了广泛的关注.我们使用纯粹的贝叶斯方法处理成分个数未知的混合回归模型中的变量选择问题.针对混合模型MCMC抽样时产生的变维问题,我们使用可逆跳MCMC的手法,给出了相应的抽样方案,使得确定混合成分个数、挑选预测变量、聚类观测个体三项任务同时完成.我们还进一步研究了使用不同的模型结构对混合回归模型变量选择的影响,以及适用的范围,并考察了当预测变量间存在共线关系时各种模型的执行情况.我们的研究结果显示出所提出的这种MCMC抽样设计是可行的,并且如果纯粹地从变量的挑选结果这一角度出发,与其它方法相比,这种贝叶斯手法的表现的是比较令人满意的.更多还原

【Abstract】 Model selection is a important part of statistical analysis, and also is an centerof general scienti?c work. Researchers hope for detecting a model which describethe data characteristic as far as possible, and subsequent work is based on thehypothesis that the data are generated from it. Therefor model selection plays animportant role in statistical analysis. From frequentist and Bayesian perspectives,many statisticians consider how to choose models, and have proposed substantivemethods. This dissertation is mainly carried out on model selection.In the study of modern medicine, scienti?c conclusions are obtained by sta-tistical analysis. Here we ?rst deal with two sets of data in drug toxicity research,and consider whether the proposed dose-response functions or models are ade-quate. These two sets of data are continuous and discrete respectively: in theformer we consider grouping patients based on drug susceptibility, in the latterthe dose-response relationship between patients and drug. The Bayes factor andcross-validation are used to select model. However, exact computation of the Bayesfactor is usually di?cult and sometimes impossible. Here we utilize the connectionbetween the Bayes factor and the Bayesian information criterion announced bySchwarz criterion, and approximate the former by latter. Medical research is to in-volve people life, therefor to choose a proper model is very important for follow-uprisk assessment.Other main work in the dissertation is to research variable selection. Mixturemodels ?exibly describe the potential heterogeneity in data, at the same time, aamount of attention has devoted to its especial model structure. Here a purityBayesian method is used for the problem of jointly selecting the number of com-ponents and variables as well as clustering heterogeneous data in ?nite mixture regression models. For the dimensionality change, an e?cient Bayesian methodvia the reversible jump Markov chain Monte Carlo algorithm is developed. Fur-ther, we consider a di?erent model structure and compare it with aforementionedmethod, specially, when there is collinearity in predictor variables. Monte Carlosimulation studies show that the proposed Markov chain Monte Carlo procedure isfeasible, and the performances of these method, comparing with other methods, issatisfactory if only consider the results of choosing variables.更多还原