Related papers: On The Distribution of Bayesian Evidences
The ratio of Bayesian evidences is a popular tool in cosmology to compare different models. There are however several issues with this method: Bayes' ratio depends on the prior even in the limit of non-informative priors, and Jeffrey's…
We discuss the use of the Bayesian evidence ratio, or Bayes factor, for model selection in astronomy. We treat the evidence ratio as a statistic and investigate its distribution over an ensemble of experiments, considering both simple…
Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of…
Bayesian model comparison is often based on the posterior distribution over the set of compared models. This distribution is often observed to concentrate on a single model even when other measures of model fit or forecasting ability…
Summary statistics of the likelihood, such as the Bayesian evidence, offer a principled way of comparing models and assessing tension between, or within, the results of physical experiments. Noisy realisations of the data induce scatter in…
We describe a new method for evaluating Bayes factors. The key idea is to introduce a hypermodel in which the competing models are components of a mixture distribution. Inference for the mixing probabilities then yields estimates of the…
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…
Bayes factors are characterized by both the powerful mathematical framework of Bayesian statistics and the useful interpretation as evidence quantification. Former requires a parameter distribution that changes by seeing the data, latter…
In Bayesian hypothesis testing, evidence for a statistical model is quantified by the Bayes factor, which represents the relative likelihood of observed data under that model compared to another competing model. In general, computing Bayes…
Both the Bayes factor and the relative belief ratio satisfy the principle of evidence and so can be seen to be valid measures of statistical evidence. Certainly Bayes factors are regularly employed. The question then is: which of these…
Inferences about hypotheses are ubiquitous in the cognitive sciences. Bayes factors provide one general way to compare different hypotheses by their compatibility with the observed data. Those quantifications can then also be used to choose…
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 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…
Gibbs random fields play an important role in statistics. However they are complicated to work with due to an intractability of the likelihood function and there has been much work devoted to finding computational algorithms to allow…
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…
In the context of Bayesian factor analysis, it is possible to compute mean plausible values, which might be used as covariates or predictors or in order to provide individual scores for the Bayesian latent variables. Previous simulation…
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…
Bayesian evidence ratios give a very attractive way of comparing models, and being able to quote the odds on a particular model seems a very clear motivation for making a choice. Jeffreys' scale of evidence is often used in the…
Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalising constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and…
Some scientific research questions ask to guide decisions and others do not. By their nature frequentist hypothesis-tests yield a dichotomous test decision as result, rendering them rather inappropriate for latter types of research…