Bayes factor consistency in regression problems
نویسندگان
چکیده
We investigate the asymptotic behavior of the Bayes factor for regression problems in which observations are not required to be independent and identically distributed and provide general results about consistency of the Bayes factor. Then we specialize our results to the model selection problem in the context of partially linear regression model in which the regression function is assumed to be the additive form of the linear component and the nonparametric component. Specifically, sufficient conditions to ensure Bayes factor consistency are given for choosing between the parametric model and the semiparametric alternative in the partially linear regression model.
منابع مشابه
Consistency of Objective Bayes Factors as the Model Dimension Grows
In the class of normal regression models with a finite number of regressors, and for a wide class of prior distributions, a Bayesian model selection procedure based on the Bayes factor is consistent [Casella and Moreno J. Amer. Statist. Assoc. 104 (2009) 1261–1271]. However, in models where the number of parameters increases as the sample size increases, properties of the Bayes factor are not t...
متن کاملA Note on the Consistency of Bayes Factors for Testing Point Null versus Nonparametric Alternatives
When testing a point null hypothesis versus an alternative that is vaguely speci ed, a Bayesian test usually proceeds by putting a non-parametric prior on the alternative and then computing a Bayes factor based on the observations. This paper addresses the question of consistency, that is, whether the Bayes factor is correctly indicative of the null or the alternative as the sample size increas...
متن کامل2 The Dirichlet process , related priors and posterior asymptotics
Here we review the role of the Dirichlet process and related prior distribtions in nonparametric Bayesian inference. We discuss construction and various properties of the Dirichlet process. We then review the asymptotic properties of posterior distributions. Starting with the definition of posterior consistency and examples of inconsistency, we discuss general theorems which lead to consistency...
متن کاملOn the Consistency of Bayes Factors for Testing Point Null versus Nonparametric Alternatives
When testing a point null hypothesis versus an alternative that is vaguely speciied, a Bayesian test usually proceeds by putting a nonparametric prior on the alternative and then computing a Bayes factor based on the observations. This paper addresses the question of consistency, that is, whether the Bayes factor is correctly indicative of the null or the alternative as sample size increases. W...
متن کاملA Bayes factor with reasonable model selection consistency for ANOVA model
Abstract: For the balanced ANOVA setup, we propose a new closed form Bayes factor without integral representation, which is however based on fully Bayes method, with reasonable model selection consistency for two asymptotic situations (either number of levels of the factor or number of replication in each level goes to infinity). Exact analytical calculation of the marginal density under a spec...
متن کامل