The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
Facilitating the Gibbs Sampler: The Gibbs Stopper and the Griddy-Gibbs Sampler
Abstract
The article briefly reviews the history, literature, and form of the Gibbs sampler. An importance sampling device is proposed for converting the output of the Gibbs sampler to a sample from the exact posterior. This Gibbs stopper technique is also useful for assessing convergence of the Gibbs sampler for moderate sized problems. Also presented is an approach for implementing the Gibbs sampler in nonconjugate situations. The basic idea is to approximate the true cdf of each conditional distribution by a piecewise linear function and then sample from the approximation. Questions relating to the number of nodes in the approximation, gap size between successive nodes, and the treatment of unbounded intervals for a given conditional are discussed. The methodology is illustrated using a genetic linkage model, a nonlinear regression model, and the Cox model.
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Cites
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Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.
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Monte Carlo sampling methods using Markov chains and their applications.
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Cited by
Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review
Cowles, M. K., & Carlin, B. P. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476956 · Cited by 2,056
Marginal Likelihood from the Gibbs Output
Chib, S. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476635 · Cited by 1,905
A hierarchical regression approach to meta‐analysis of diagnostic test accuracy evaluations
Rutter, C. M., & Gatsonis, C. A. (2001) · Statistics in Medicine · doi:10.1002/sim.942 · Cited by 1,505
Markov chain Monte Carlo method and its application
Brooks, S. (1998) · Journal of the Royal Statistical Society: Series D (The Statistician) · doi:10.1111/1467-9884.00117 · Cited by 843
The dynamics of stochastic volatility: evidence from underlying and options markets
Jones, C. S. (2003) · Journal of Econometrics · doi:10.1016/s0304-4076(03)00107-6 · Cited by 503
Metadata
- Authors
- Ritter, C., & Tanner, M. A.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1992-09
- Volume
- 87
- Issue
- 419
- Pages
- 861-868
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2038429130
- Cited by
- 425
- References
- 25
- FWCI
- 13.78
- Type
- journal article
- Language
- en
- Open access
- closed
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- Ritter, C., & Tanner, M. A. (1992). Facilitating the Gibbs Sampler: The Gibbs Stopper and the Griddy-Gibbs Sampler. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1992.10475289
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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.
