Related papers: Simple Bayesian testing of scientific expectations…
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…
Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…
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…
This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…
The random-effects or normal-normal hierarchical model is commonly utilized in a wide range of meta-analysis applications. A Bayesian approach to inference is very attractive in this context, especially when a meta-analysis is based only on…
A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter $\theta_j$ was equal or lay close to a specified value…
Experiments in research on memory, language, and in other areas of cognitive science are increasingly being analyzed using Bayesian methods. This has been facilitated by the development of probabilistic programming languages such as Stan,…
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…
We propose a Bayesian propensity score-augmented latent factor model for causal inference with time-series cross-sectional data. The framework explicitly models the treatment assignment mechanism by incorporating latent factor loadings,…
Scientific claims gain credibility by replicability, especially if replication under different circumstances and varying designs yields equivalent results. Aggregating results over multiple studies is, however, not straightforward, and when…
Two procedures for checking Bayesian models are compared using a simple test problem based on the local Hubble expansion. Over four orders of magnitude, p-values derived from a global goodness-of-fit criterion for posterior probability…
This paper introduces a feasible and practical Bayesian method for unit root testing in financial time series. We propose a convenient approximation of the Bayes factor in terms of the Bayesian Information Criterion as a straightforward and…
This paper introduces the R package BayesVarSel which implements objective Bayesian methodology for hypothesis testing and variable selection in linear models. The package computes posterior probabilities of the competing hypotheses/models…
We investigate the discrimination of two candidates of an unknown parameter in quantum systems with continuous weak measurement, inspired by the application of hypothesis testing in distinguish-ing two Hamiltonians [Kiilerich and M{\o}lmer,…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
In observational studies, the propensity score plays a central role in estimating causal effects of interest. The inverse probability weighting (IPW) estimator is commonly used for this purpose. However, if the propensity score model is…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
Experiments on decision making under uncertainty are known to display a classical pattern of risk aversion and risk seeking referred to as "fourfold pattern" (or "reflection effect") , but recent experiments varying the speed and order of…
Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…
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…