The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index.
Explaining the Gibbs Sampler
Abstract
Computer-intensive algorithms, such as the Gibbs sampler, have become increasingly popular statistical tools, both in applied and theoretical work. The properties of such algorithms, however, may sometimes not be obvious. Here we give a simple explanation of how and why the Gibbs sampler works. We analytically establish its properties in a simple case and provide insight for more complicated cases. There are also a number of examples.
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Citations
Cites
Maximum Likelihood from Incomplete Data Via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444
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
Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.
Geman, S., & Geman, D. (1984) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.1984.4767596 · Cited by 17,949
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
The Jackknife, the Bootstrap and Other Resampling Plans
Efron, B. (1982) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970319 · Cited by 8,120
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
Spatial Interaction and the Statistical Analysis of Lattice Systems
Besag, J. (1974) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1974.tb00999.x · Cited by 6,067
Maximum likelihood estimation from incomplete data via the EM algorithm
Dempster, A. P. (1977) · Journal of the Royal Statistical Society Series A (Statistics in Society) · Cited by 4,543
Non-Uniform Random Variate Generation
Devroye, L. (1986) · Springer eBooks · doi:10.1007/978-1-4613-8643-8 · Cited by 4,041
The Calculation of Posterior Distributions by Data Augmentation
Tanner, M. A., & Wong, W. H. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478458 · Cited by 3,928
Cited by
Discrete Choice Methods with Simulation
Train, K. E. (2001) · doi:10.1017/cbo9780511805271 · Cited by 7,784
F. Dormann, C., M. McPherson, J., B. Araújo, M., Bivand, R., Bolliger, J., Carl, G., G. Davies, R., Hirzel, A., Jetz, W., Daniel Kissling, W., et al. (2007) · Ecography · doi:10.1111/j.2007.0906-7590.05171.x · Cited by 3,433
Variable Selection via Gibbs Sampling
George, E. I., & McCulloch, R. E. (1993) · Journal of the American Statistical Association · doi:10.1080/01621459.1993.10476353 · Cited by 2,828
Self-citationStructural Equation Modeling and Natural Systems
Grace, J. B. (2006) · doi:10.1017/cbo9780511617799 · Cited by 2,432
Deep Learning in Mobile and Wireless Networking: A Survey
Zhang, C., Patras, P., & Haddadi, H. (2019) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2019.2904897 · Cited by 1,768
Metadata
- Authors
- Casella, G., & George, E. I.
- Venue
- The American Statistician
- Publisher
- Informa UK Limited
- Published
- 1992-08
- Volume
- 46
- Issue
- 3
- Pages
- 167-174
- ISSN
- 0003-1305 (ISSN-L)
- 1537-2731
- OpenAlex
- W2163738067
- Cited by
- 2,364
- References
- 33
- FWCI
- 30.31
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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