Bayesian Computation†
First published: 15 January 2013
†
Based in part on the article “Bayesian computation” by Alan Gelfand, which appeared in the Encyclopedia of Environmetrics.
No abstract is available for this article.
References
- 1 Smith, A.F.M., Skene, A.M., Shaw, J.E.H., Naylor, J.C., & Dransfield, M. (1985). The implememntation o the Bayesian paradigm, Communications in Statistics: Theory and Methods, 14, 1079–1109.
- 2 Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis, Springer-Verlag, New York.
- 3 Kass, R.E., Tierney, L., & Kadane, J.B. (1989). The validity of posterior expansions based on Laplace's method, in Bayesian and Likelihood Methods in Statistics and Economics: Essays in Honor of George A. Barnard, S. Geisser, J.S. Hodges, S.J. Press, & A. Zellner, eds, North-Holland, Amsterdam, pp. 473–488.
- 4
Kass, R.E.,
Tierney, L., &
Kadane, J.B.
(1991).
Laplace's method in Bayesian analysis, in
Statistical Multiple Integration,
N. Fluornoy &
R.K. Tsutukawa, eds,
American Statistical Association,
Providence, pp.
89–99.
10.1090/conm/115/07 Google Scholar
- 5 Rue, H., Martino, S., & Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations, Journal of the Royal Statistical Society, B, 71, 1–35.
- 6
Carlin, B.P. &
Louis, T.A.
(2000).
Bayes and Empirical Bayes Methods for Data Analysis,
2nd Edition,
Chapman & Hall,
London.
10.1201/9781420057669 Google Scholar
- 7 Gelman, A., Carlin, J.B., Stern, H.S., & Rubin, D.B. (2004). Bayesian Data Analysis, 2nd Edition, Chapman & Hall, London.
- 8
Gilks, W.R.,
Richardson, S., &
Spiegelhalter, D.J.
(1995).
Markov Chain Monte Carlo in Practice,
Chapman & Hall,
London.
10.1201/b14835 Google Scholar
- 9 Geweke, J. (1989). Bayesian inference in econometric models using Monte Carlo integration, Econometrica 57, 1317–1339.
- 10
Robert, C.P. &
Casella, G.
(2004).
Monte Carlo Statistical Methods,
2nd Edition,
Springer-Verlag,
New York.
10.1007/978-1-4757-4145-2 Google Scholar
- 11 Smith, A.F.M. & Gelfand, A.E. (1992). Bayesian statistics without tears: a sampling resampling perspective, The American Statistician 46, 84–88.
- 12 Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–740.
- 13 Gelfand, A.E. & Smith, A.F.M. (1990). Sampling based approaches to calculating marginal densities, Journal of the American Statistical Association 85, 398–409.
- 14 Cappé, O., Godsill, S.J., & Moulines, E. (2007). An overview of existing methods and recent advances in sequential Monte Carlo, IEEE Proceedings 95(5), 899–924.
- 15
A. Doucet,
N. deFreitas, &
N.J. Gordon, eds.
(2001).
Sequential Monte Carlo Methods in Practice,
Springer-Verlag,
New York.
10.1007/978-1-4757-3437-9 Google Scholar
- 16 Carvalho, C.M., Johannes, M.S., Lopes, H.F., & Polson, N.G. (2010). Particle Learning and Smoothing, Statistical Science 25(1), 88–106.
- 17 Ormerod, J.T. & Wand, M.P. (2010). Explaining variational approximations, The American Statistician, 64, 140–153.
- 18 Beaumont, M.A., Zhang, W., & Balding, D.J. (2002). Approximate bayesian computation in population genetics, Genetics, 162(4), 2025–2035.
- 19 Marjoram, P., Molitor, J., Plagnol, V., & Tavaré, S. (2003). Markov chain Monte Carlo without likelihoods, Proceedings of the National Academy of Sciences 100(26), 15324–15328.