Computing Bayes: From Then 'Til Now'
Abstract
This paper takes the reader on a journey through the history of Bayesian computation, from the 18th century to the present day. Beginning with the one-dimensional integral first confronted by Bayes in 1763, we highlight the key contributions of: Laplace, Metropolis (and, importantly, his co-authors!), Hammersley and Handscomb, and Hastings, all of which set the foundations for the computational revolution in the late 20th century -- led, primarily, by Markov chain Monte Carlo (MCMC) algorithms. A very short outline of 21st century computational methods -- including pseudo-marginal MCMC, Hamiltonian Monte Carlo, sequential Monte Carlo, and the various `approximate' methods -- completes the paper.
Cite
@article{arxiv.2208.00646,
title = {Computing Bayes: From Then 'Til Now'},
author = {Gael M. Martin and David T. Frazier and Christian P. Robert},
journal= {arXiv preprint arXiv:2208.00646},
year = {2023}
}
Comments
Material that appeared in an earlier paper, `Computing Bayes: Bayesian Computation from 1763 to the 21st Century' (arXiv:2004.06425) has been broken up into two separate papers: this historical overview of, and timeline for, all computational developments is retained; and a secondary paper (arXiv:2112.10342), which provides a more detailed review of 21st century