Statistical inference with exchangeability and martingales

Journal article

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’.

Authors: Holmes, CC; Walker, SG

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: The Royal Society
• Journal: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Volume: 381
• Issue: 2247
• Pages: 20220143
• Article number: 20220143
• Publication date: 2023-03-27
• Acceptance date: 2023-01-30
• DOI: 10.1098/rsta.2022.0143
• EISSN: 1471-2962
• ISSN: 1364503X, 1364-503X
• Language: English
• Keywords: bootstrap; parametric bootstrap; score function; predictive inference