An important aspect of mixture modeling concerns the selection of the number of mixture components. In this paper, we discuss the Bayes factor as a selection tool. The discussion will focus on two aspects: (i) computation of the Bayes factor and (ii) prior sensitivity. For the computation, we propose a variant of Chib’s estimator that accounts for the non-identifiability of the mixture componen...

The Bayes factor is a useful tool for evaluating sets of inequality and about equality constrainedmodels. In the approach described, the Bayes factor for a constrained model with the encompassing model reduces to the ratio of two proportions, namely the proportion of, respectively, the encompassing prior and posterior in agreement with the constraints. This enables easy and straightforward esti...

In Bayesian model selection or testing problems, Bayes factors under proper priors have been very successful. In practice, however, limited information and time constraints often require us to use noninformative priors which are typically improper and are deened only up to arbitrary constants. The resulting Bayes factors are then not well deened. A recently proposed model selection criterion, t...

INTRODUCTION Most of the experiments to map QTLs involve recording of several traits, often genetically correlated between them. Several authors have tried to solve the problem of discriminating between linked and pleiotropic QTLs (Cheverud et al., 1997 ; Almasy et al., 1997 ; Lebreton et al., 1998 ; Knott and Haley, 2000). From a bayesian point of view, the comparison between alternative model...

This paper proposes Bayesian methods for estimating the cointegration rank using Bayes factors. We consider natural conjugate priors for computing Bayes factors. First, we estimate the cointegrating vectors for each possible rank. Then, we compute the Bayes factors for each rank against 0 rank. Monte Carlo simulations show that using Bayes factor with conjugate priors produces fairly good resul...

Differences in treatment effects between centers in a multi-center trial may be important. These differences represent treatment by subgroup interaction. Peto defines qualitative interaction (QI) to occur when the simple treatment effect in one subgroup has a different sign than in another subgroup: this interaction is important. Interaction where the treatment effects are of the same sign in a...

We discuss the definition of a Bayes factor, the Savage-Dickey result, and develop some inequalities relevant to Bayesian inferences. We consider the implications of these inequalities for the Bayes factor approach to hypothesis assessment. An approach to hypothesis assessment based on the computation of a Bayes factor, a measure of reliability of the Bayes factor, and the point where the Bayes...