Practical markov chain monte carlo
Open accessAbstract
Markov chain Monte Carlo using the Metropolis-Hastings algorithm is a general method for the simulation of stochastic processes having probability densities known up to a constant of proportionality. Despite recent advances in its theory, the practice has remained controversial. This article makes the case for basing all inference on one long run of the Markov chain and estimating the Monte Carlo error by standard nonparametric methods well-known in the time-series and operations research literature. In passing it touches on the Kipnis-Varadhan central limit theorem for reversible Markov chains, on some new variance estimators, on judging the relative efficiency of competing Monte Carlo schemes, on methods for constructing more rapidly mixing Markov chains and on diagnostics for Markov chain Monte Carlo.
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MCMC methods can sample directly from any arbitrary probability density function which is known up to a normalizing constant.
“This class of methods can sample directly from any arbitrary probability density function which is known up to a normalizing constant [74].”
From Parameter uncertainty in biochemical models described by ordinary differential equations (2013) · cites this paper as [74]
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- Authors
- Geyer, C. J.
- Affiliations
- University of Minnesota (US)
- Corresponding author
- Geyer, Charles J.
- ORCID
- Geyer, Charles J.
- Venue
- Statistical Science
- Publisher
- Institute of Mathematical Statistics
- Published
- 1992-11-01
- Volume
- 7
- Issue
- 4
- Pages
- 473-483
- ISSN
- 0883-4237 (ISSN-L)
- 2168-8745
- OpenAlex
- W2048971218
- Cited by
- 2,045
- References
- 49
- Citations by year
- 2026: 50 · 2025: 80 · 2024: 82 · 2023: 72 · 2022: 116 · 2021: 105 · 2020: 87 · 2019: 79 · 2018: 64 · 2017: 77 · 2016: 93 · 2015: 82 · 2014: 95 · 2013: 79 · 2012: 82
- FWCI
- 24.57
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Statistical Science (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Social Sciences › Decision Sciences › Management Science and Operations Research › Simulation Techniques and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- Markov chain Monte Carlo, Metropolis-Hastings algorithm, Monte Carlo error estimation, nonparametric variance estimation, reversible Markov chains, variance estimators, Markov chain mixing, MCMC diagnostics, Bayesian inference
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