The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Markov Chains for Exploring Posterior Distributions
Open accessAbstract
Several Markov chain methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm. In addition, several strategies are available for constructing hybrid algorithms. This paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues. On the theoretical side, results from the theory of general state space Markov chains can be used to obtain convergence rates, laws of large numbers and central limit theorems for estimates obtained from Markov chain methods. These theoretical results can be used to guide the construction of more efficient algorithms. For the practical use of Markov chain methods, standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation.
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
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
Cited by
MRBAYES: Bayesian inference of phylogenetic trees.
Huelsenbeck, J. P., & Ronquist, F. (2001) · Bioinformatics · doi:10.1093/bioinformatics/17.8.754 · Cited by 21,937
General methods for monitoring convergence of iterative simulations
Brooks, S. P., & Gelman, A. (1998) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.1998.10474787 · Cited by 6,045
Bayesian Inference of Phylogeny and Its Impact on Evolutionary Biology
Huelsenbeck, J. P., Ronquist, F., Nielsen, R., & Bollback, J. P. (2001) · Science · doi:10.1126/science.1065889 · Cited by 2,737
An introduction to MCMC for machine learning.
Andrieu, C., de Freitas, N., Doucet, A., & Jordan, M. I. (2003) · Machine Learning · doi:10.1023/a:1020281327116 · Cited by 2,451
Casella, G., & George, E. I. (1992) · The American Statistician · doi:10.1080/00031305.1992.10475878 · Cited by 2,364
Metadata
- Authors
- Tierney, L.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1994-12-01
- Volume
- 22
- Issue
- 4
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2136796925
- Cited by
- 3,452
- References
- 2
- FWCI
- 83.90
- Type
- journal article
- Language
- en
- Open access
- bronze
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: Markov Chains for Exploring Posterior Distributions. https://app.cochat.ai/papers/10.1214/aos/1176325750
- The paper
- Tierney, L. (1994). Markov Chains for Exploring Posterior Distributions. The Annals of Statistics. https://doi.org/10.1214/aos/1176325750
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.
