Statistical inference with exchangeability and martingales-Reference-Cited by-同舟云学术

Statistical inference with exchangeability and martingales

Published:2023-03-27 Issue:2247 Volume:381 Page:
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Holmes Chris C.¹^ORCID,Walker Stephen G.²³

Affiliation:

1. Department of Statistics, University of Oxford, Oxford, UK

2. Department of Mathematics, University of Texas at Austin, Austin, TX, USA

3. Department of Statistics & Scientific Computation, University of Texas at Austin, Austin, TX, USA

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’.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2022.0143

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