Related papers: Hierarchical inference of evidence using posterior…

Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…

Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…

We classify two types of Hierarchical Bayesian Model found in the literature as Hierarchical Prior Model (HPM) and Hierarchical Stochastic Model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of…

Parameter estimates for associated genetic variants, report ed in the initial discovery samples, are often grossly inflated compared to the values observed in the follow-up replication samples. This type of bias is a consequence of the…

Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…

We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models…

This article presents new methodology for sample-based Bayesian inference when data are partitioned and communication between the parts is expensive, as arises by necessity in the context of "big data" or by choice in order to take…

Usually one compares the accuracy of two competing classifiers via null hypothesis significance tests (nhst). Yet the nhst tests suffer from important shortcomings, which can be overcome by switching to Bayesian hypothesis testing. We…

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…

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…

Comparison of appropriate models to describe observational data is a fundamental task of science. The Bayesian model evidence, or marginal likelihood, is a computationally challenging, yet crucial, quantity to estimate to perform Bayesian…

The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…

Model-based diagnosis reasons backwards from a functional schematic of a system to isolate faults given observations of anomalous behavior. We develop a fully probabilistic approach to model based diagnosis and extend it to support…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

The model evidence is a vital quantity in the comparison of statistical models under the Bayesian paradigm. This paper presents a review of commonly used methods. We outline some guidelines and offer some practical advice. The reviewed…

Hierarchical models are increasingly used in many applications. Along with this increased use comes a desire to investigate whether the model is compatible with the observed data. Bayesian methods are well suited to eliminate the many…

Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…

This paper considers the problem of making statistical inferences about a parameter when a narrow interval centred at a given value of the parameter is considered special, which is interpreted as meaning that there is a substantial degree…

To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into…