Computing Bayes: From Then 'Til Now'
arXiv:2208.00646 · doi:10.1214/22-STS876
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.
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
References in corpus (9)
- The pseudo-marginal approach for efficient Monte Carlo computations
- On Markov chain Monte Carlo methods for tall data
- Three discussions of the paper "sequential quasi-Monte Carlo sampling", by M. Gerber and N. Chopin
- Consistency of Markov chain quasi-Monte Carlo on continuous state spaces
- MCMC Using Ensembles of States for Problems with Fast and Slow Variables such as Gaussian Process Regression
- Approximating Bayes in the 21st Century
- Integrated Nested Laplace Approximations (INLA)
- Generalized Posteriors in Approximate Bayesian Computation
- An attempt to trace the birth of importance sampling