Finite Mixture Model Selection By Bayesian Methods

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.