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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…

Bayesian likelihood-free methods implement Bayesian inference using simulation of data from the model to substitute for intractable likelihood evaluations. Most likelihood-free inference methods replace the full data set with a summary…

Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis…

We consider the problem of model choice for stochastic epidemic models given partial observation of a disease outbreak through time. Our main focus is on the use of Bayes factors. Although Bayes factors have appeared in the epidemic…

Across the empirical sciences, few statistical procedures rival the popularity of the frequentist t-test. In contrast, the Bayesian versions of the t-test have languished in obscurity. In recent years, however, the theoretical and practical…

Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…

In the Bayesian literature on model comparison, Bayes factors play the leading role. In the classical statistical literature, model selection criteria are often devised used cross-validation ideas. Amalgamating the ideas of Bayes factor and…

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…

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…

This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…

Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We…

Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian computation (ABC) is a method of inference for…

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…

In this paper we derive an explicit formula for calculating the marginal likelihood of a given factorization of a categorical dataset. Since the marginal likelihood is proportional to the posterior probability of the factorization, these…

Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…

Many modern statistical applications involve inference for complicated stochastic models for which the likelihood function is difficult or even impossible to calculate, and hence conventional likelihood-based inferential echniques cannot be…

This paper, which is Part 1 of a two-part paper series, considers a simulation-based inference with learned summary statistics, in which such a learned summary statistic serves as an empirical-likelihood with ameliorative effects in the…

Bayes factor null hypothesis tests provide a viable alternative to frequentist measures of evidence quantification. Bayes factors for realistic data sets in areas like psychology cannot be calculated exactly and require numerical…

Using instruments comprising ordered responses to items are ubiquitous for studying many constructs of interest. However, using such an item response format may lead to items with response categories infrequently endorsed or unendorsed…

Bayesian statistics is an integral part of contemporary applied science. bayesics provides a single framework, unified in syntax and output, for performing the most commonly used statistical procedures, ranging from one- and two-sample…