Student or educator? Sign up with your school email and get 6 months of Pro free.
Cited by 4,145

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

Chib, Siddhartha, Greenberg, Edward·1995·The American Statistician

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.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1080/00031305.1995.10476177

Cites

6 of 6 references verified0 citation errors · 0 not checkable

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.

A few free checks a day · papers already verified open instantly · results are public

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

Show all 6 references

Research works printed but not linked: 19

  1. Bhattacharya R. N., 1900, Stochastic Processes with Applications
  2. Billingsley P., 1986, Probability and Measure,
  3. Box G. E. P., 1976, Time Series Analysis: Forecasting and Control,
  4. 10.1080/00031305.1992.10475878 · DOI · Paper page
  5. Chib S., 1993, Econometric Theory
  6. 10.1016/0304-4076(94)90063-9 · DOI · Paper page
  7. Dagpunar J., 1988, Principles of Random Variate Generation
  8. Gelman, A. “Iterative and Non-Iterative Simulation Algorithms”. Computing Science and Statistics (Interface Proceedings). Vol. 24, pp.433–438.
  9. 10.1214/ss/1177011136 · DOI · Paper page
  10. 10.2307/1913710 · DOI · Paper page
  11. Meyn S. P., 1993, Markov Chains and Stochastic Stability, 10.1007/978-1-4471-3267-7 · DOI · Paper page
  12. Müller P., 1993, “A Generic Approach to Posterior Integration and Gibbs Sampling”
  13. 10.1017/CBO9780511526237 · DOI · Paper page
  14. 10.2307/2290978 · doi:10.2307/2290978
  15. Roberts G. O., 1994, “Geometric Convergence and Central Limit Theorems for Multidimensional Hastings and Metropolis Algorithms”
  16. 10.1002/9780470316511 · DOI
  17. Tanner M. A., 1993, Tools for Statistical Inference,, 10.1007/978-1-4684-0192-9 · DOI · Paper page
  18. 10.1080/01621459.1987.10478458 · DOI · Paper page
  19. 10.1214/aos/1176325750 · DOI · Paper page

Cited by

See all 4,145

Metadata

Authors
Chib, S., & Greenberg, E.
Venue
The American Statistician
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.