Related papers: How accurate are Bayes factor-based null hypothesi…
We propose and evaluate two methods that validate the computation of Bayes factors: one based on an improved variant of simulation-based calibration checking (SBC) and one based on calibration metrics for binary predictions. We show that in…
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…
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 hypothesis testing via Bayes factors offers a principled alternative to classical p-value methods in meta-analysis, particularly suited to its cumulative and sequential nature. Unlike commonly reported p-values for standard null…
Bayesian linear mixed-effects models and Bayesian ANOVA are increasingly being used in the cognitive sciences to perform null hypothesis tests, where a null hypothesis that an effect is zero is compared with an alternative hypothesis that…
Verifying the correctness of Bayesian computation is challenging. This is especially true for complex models that are common in practice, as these require sophisticated model implementations and algorithms. In this paper we introduce…
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…
To check the accuracy of Bayesian computations, it is common to use rank-based simulation-based calibration (SBC). However, SBC has drawbacks: The test statistic is somewhat ad-hoc, interactions are difficult to examine, multiple testing is…
Simulation-based calibration checking (SBC) is a practical method to validate computationally-derived posterior distributions or their approximations. In this paper, we introduce a new variant of SBC to alleviate several known problems. Our…
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 an increasingly popular tool for indexing evidence from experiments. For two competing population models, the Bayes factor reflects the relative likelihood of observing some data under one model compared to the other. In…
Determining an appropriate sample size is a critical element of study design, and the method used to determine it should be consistent with the planned analysis. When the planned analysis involves Bayes factor hypothesis testing, the sample…
The Bayes factor, the data-based updating factor from prior to posterior odds, is a principled measure of relative evidence for two competing hypotheses. It is naturally suited to sequential data analysis in settings such as clinical trials…
Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…
We present a new test of hypothesis in which we seek the probability of the null conditioned on the data, where the null is a simplification undertaken to counter the intractability of the more complex model, that the simpler null model is…
Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. Drawbacks of Bayes factors are their dependence on prior specifications that define null and alternative hypotheses and difficulties…
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…
Random effects are a flexible addition to statistical models to capture structural heterogeneity in the data, such as spatial dependencies, individual differences, temporal dependencies, or non-linear effects. Testing for the presence (or…
In this paper, I develop a formula for estimating Bayes factors directly from minimal summary statistics produced in repeated measures analysis of variance designs. The formula, which requires knowing only the $F$-statistic, the number of…
Bayesian sample size calculations in clinical trials usually rely on complex Monte Carlo simulations in practice. Obtaining bounds on Bayesian notions of the false-positive rate and power often lack closed-form or approximate numerical…