In this article, we present a Bayes factor solution for inference in multiple regression. Bayes factors are principled measures of the relative evidence from data for various models or positions, including models that embed null hypotheses. In this regard, they may be used to state positive evidence for a lack of an effect, which is not possible in conventional significance testing. One obstacl...

The posterior distribution of the likelihood is used to interpret the evidential meaning of P-values, posterior Bayes factors and Akaike's information criterion when comparing point null hypotheses with composite alternatives. Asymptotic arguments lead to simple re-calibrations of these criteria in terms of posterior tail probabilities of the likelihood ratio. (`Prior') Bayes factors cannot be ...

In this paper, we present a Bayes factor solution for inference in multiple regression. Bayes factors are principled measures of the relative evidence from data for various models or positions, including models that embed null hypotheses. In this regard, they may be used to state positive evidence for a lack of an effect, which is not possible in conventional significance testing. One obstacle ...

Bayes factors have been ooered by Bayesians as alternatives to P-values (or significance probabilities) for testing hypotheses and for quantifying the degree to which observed data support or connict with a hypothesis. Schervish (1996) showed how the interpretation of P-values as measures of support suuers a certain logical aw. In this paper, we show how Bayes factors suuer that same aw. We inv...

The Bayes factor is employed to select covariates for a hierarchical model applied to a collection of hospital admission counts. Integrals representing the Bayes factor numerator and denominator marginal probabilities are intractable for the model used. We examine three approaches to integral approximation: Laplace approximation, Monte Carlo integration, and a Markov chain Monte Carlo (MCMC) ap...

The Bayes factor is an intuitive and principled model selection tool from Bayesian statistics. The Bayes factor quantifies the relative likelihood of the observed data under two competing models, and as such, it measures the evidence that the data provides for one model versus the other. Unfortunately, computation of the Bayes factor often requires sampling-based procedures that are not trivial...

We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a nonparametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular densities. Running headline: Bayesian Goodness of Fit Testing

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 b...