The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
Understanding the Metropolis-Hastings Algorithm
Abstract
We provide a detailed, introductory exposition of the Metropolis-Hastings algorithm, a powerful Markov chain method to simulate multivariate distributions. A simple, intuitive derivation of this method is given along with guidance on implementation. Also discussed are two applications of the algorithm, one for implementing acceptance-rejection sampling when a blanketing function is not available and the other for implementing the algorithm with block-at-a-time scans. In the latter situation, many different algorithms, including the Gibbs sampler, are shown to be special cases of the Metropolis-Hastings algorithm. The methods are illustrated with examples.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Equation of State Calculations by Fast Computing Machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192
Monte Carlo sampling methods using Markov chains and their applications.
Hastings, W. K. (1970) · Biometrika · doi:10.1093/biomet/57.1.97 · Cited by 15,195
Sampling-based approaches to calculating marginal densities
Gelfand, A. E., & Smith, A. F. M. (1990) · Journal of the American Statistical Association · doi:10.1080/01621459.1990.10476213 · Cited by 6,606
Simulation and the Monte Carlo Method
Rubinstein, R. Y., & Kroese, D. P. (2016) · Wiley Series in Probability and Statistics · doi:10.1002/9781118631980 · Cited by 3,356
Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods
Smith, A. F. M., & Roberts, G. O. (1993) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1993.tb01466.x · Cited by 1,713
Weak convergence and optimal scaling of random walk Metropolis algorithms
Roberts, G. O., Gelman, A., & Gilks, W. R. (1997) · The Annals of Applied Probability · doi:10.1214/aoap/1034625254 · Cited by 1,693
Research works printed but not linked: 19
- Bhattacharya R. N., 1900, Stochastic Processes with Applications
- Billingsley P., 1986, Probability and Measure,
- Box G. E. P., 1976, Time Series Analysis: Forecasting and Control,
- 10.1080/00031305.1992.10475878 · DOI · Paper page
- Chib S., 1993, Econometric Theory
- 10.1016/0304-4076(94)90063-9 · DOI · Paper page
- Dagpunar J., 1988, Principles of Random Variate Generation
- Gelman, A. “Iterative and Non-Iterative Simulation Algorithms”. Computing Science and Statistics (Interface Proceedings). Vol. 24, pp.433–438.
- 10.1214/ss/1177011136 · DOI · Paper page
- 10.2307/1913710 · DOI · Paper page
- Meyn S. P., 1993, Markov Chains and Stochastic Stability, 10.1007/978-1-4471-3267-7 · DOI · Paper page
- Müller P., 1993, “A Generic Approach to Posterior Integration and Gibbs Sampling”
- 10.1017/CBO9780511526237 · DOI · Paper page
- 10.2307/2290978 · doi:10.2307/2290978
- Roberts G. O., 1994, “Geometric Convergence and Central Limit Theorems for Multidimensional Hastings and Metropolis Algorithms”
- 10.1002/9780470316511 · DOI
- Tanner M. A., 1993, Tools for Statistical Inference,, 10.1007/978-1-4684-0192-9 · DOI · Paper page
- 10.1080/01621459.1987.10478458 · DOI · Paper page
- 10.1214/aos/1176325750 · DOI · Paper page
Cited by
Inference of Population Structure Using Multilocus Genotype Data
Pritchard, J. K., Stephens, M., & Donnelly, P. (2000) · Genetics · doi:10.1093/genetics/155.2.945 · Cited by 33,908
Discrete Choice Methods with Simulation
Train, K. E. (2001) · doi:10.1017/cbo9780511805271 · Cited by 7,784
Hoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999) · Statistical Science · doi:10.1214/ss/1009212519 · Cited by 4,118
(1997) · Cited by 1,193
Hands-On Bayesian Neural Networks—A Tutorial for Deep Learning Users
Jospin, L. V., Laga, H., Boussaid, F., Buntine, W., & Bennamoun, M. (2022) · IEEE Computational Intelligence Magazine · doi:10.1109/mci.2022.3155327 · Cited by 879
Metadata
- Authors
- Chib, S., & Greenberg, E.
- Venue
- The American Statistician
- Publisher
- Informa UK Limited
- Published
- 1995-11
- Volume
- 49
- Issue
- 4
- Pages
- 327-335
- ISSN
- 0003-1305 (ISSN-L)
- 1537-2731
- OpenAlex
- W2108207895
- Cited by
- 4,145
- References
- 6
- FWCI
- 28.20
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Understanding the Metropolis-Hastings Algorithm. https://app.cochat.ai/papers/10.1080/00031305.1995.10476177
- The paper
- Chib, S., & Greenberg, E. (1995). Understanding the Metropolis-Hastings Algorithm. The American Statistician. https://doi.org/10.1080/00031305.1995.10476177
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.