The Bayes factor is commonly used for assessing the evidence for or against a given hypothesis H0 : θ ∈ Θ0, where Θ0 is a subset of the parameter space. In this paper we discuss the Bayes factor and various issues associated with its use. A Bayes factor is seen to be intimately connected with a relative belief ratio which provides a somewhat simpler approach to assessing the evidence in favor o...

A lot of models used to represent preferences or other relations have been characterized in the framework of measurement theory. To assess the empirical validity of one of these models, we can either test the model itself or test the axioms characterizing it. When a model is rejected, the latter approach has the advantage of indicating why it is rejected. The available statistical techniques fo...

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...

We investigate the theoretical performance of Bayes factor estimators in wavelet regression models with independent and identically distributed errors that are not necessarily normally distributed. We compare these estimators in terms of their frequentist optimality in Besov spaces for a wide variety of error and prior distributions. Furthermore, we provide sufficient conditions that determine ...

BACKGROUND AND AIMS It has been proposed that more use should be made of Bayes factors in hypothesis testing in addiction research. Bayes factors are the ratios of the likelihood of a specified hypothesis (e.g. an intervention effect within a given range) to another hypothesis (e.g. no effect). They are particularly important for differentiating lack of strong evidence for an effect and evidenc...

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...