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Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool, which has experienced a recent…

The multivariate normal linear model is one of the most widely employed models for statistical inference in applied research. Special cases include (multivariate) t testing, (M)AN(C)OVA, (multivariate) multiple regression, and repeated…

The is no other model or hypothesis verification tool in Bayesian statistics that is as widely used as the Bayes factor. We focus on generative models that are likelihood-free and, therefore, render the computation of Bayes factors…

The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…

A Bayes factor is proposed for testing whether the effect of a key predictor variable on the dependent variable is linear or nonlinear, possibly while controlling for certain covariates. The test can be used (i) when one is interested in…

In Bayesian analysis of multi-way contingency tables, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameters is a major challenge. In this paper, we define a flexible family of…

Bayes factor, defined as the ratio of the marginal likelihood functions of two competing models, is the natural Bayesian procedure for model selection. Marginal likelihoods are usually computationally demanding and complex. This scenario is…

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.…

We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…

In statistics, there are a variety of methods for performing model selection that all stem from slightly different paradigms of statistical inference. The reasons for choosing one particular method over another seem to be based entirely on…

Zellner's $g$-prior is a popular prior choice for the model selection problems in the context of normal regression models. Wang and Sun [J. Statist. Plann. Inference 147 (2014) 95-105] recently adopt this prior and put a special hyper-prior…

In practical situations, most experimental designs often yield unbalanced data which have different numbers of observations per unit because of cost constraints, or missing data, etc. In this paper, we consider the Bayesian approach to…

Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way…

A staple of Bayesian model comparison and hypothesis testing, Bayes factors are often used to quantify the relative predictive performance of two rival hypotheses. The computation of Bayes factors can be challenging, however, and this has…

In the context of testing general relativity with gravitational waves, constraints obtained with multiple events are typically combined either through a hierarchical formalism or though a combined multiplicative Bayes factor. We show that…

The Bayes factor is a widely used criterion in model comparison and its logarithm is a difference of out-of-sample predictive scores under the logarithmic scoring rule. However, when some of the candidate models involve vague priors on…

Latent factor models are the canonical statistical tool for exploratory analyses of low-dimensional linear structure for an observation matrix with p features across n samples. We develop a structured Bayesian group factor analysis model…

In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…

The quality of a Bayes factor crucially depends on the number of regressors, the sample size and the prior on the regression parameters, and hence it has to be established in a case-by-case basis. In this paper we analyze the consistency of…

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…