Statistical inference with exchangeability and martingales
Chris Holmes, Stephen G. Walker
2023Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences11 citationsDOIOpen Access PDF
Abstract
In this paper, we start by reviewing exchangeability and its relevance to the Bayesian approach. We highlight the predictive nature of Bayesian models and the symmetry assumptions implied by beliefs of an underlying exchangeable sequence of observations. By taking a closer look at the Bayesian bootstrap, the parametric bootstrap of Efron and a version of Bayesian thinking about inference uncovered by Doob based on martingales, we introduce a parametric Bayesian bootstrap. Martingales play a fundamental role. Illustrations are presented as is the relevant theory. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.
Topics & Concepts
Bayesian probabilityInferenceBayesian inferenceBayesian statisticsStatistical inferenceComputer sciencePredictive inferenceEconometricsArtificial intelligenceMathematicsFrequentist inferenceStatisticsBayesian Methods and Mixture ModelsStatistical Methods and InferenceStatistical Methods and Bayesian Inference