The Two-Stage Gibbs Sampler
The previous chapter presented the slice sampler, a special case of a Markov chain algorithm that did not need an Accept–Reject step to be valid, seemingly because of the uniformity of the target distribution. The reason why the slice sampler works is, however, unrelated to this uniformity and we will see in this chapter a much more general family of algorithms that function on the same principle. This principle is that of using the true conditional distributions associated with the target distribution to generate from that distribution.
KeywordsMarkov Chain Posterior Distribution Gibbs Sampler Joint Density Target Distribution
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- Diebolt, J. and Robert, C. (1990a). Bayesian estimation of finite mixture distributions, part I: Theoretical aspects. Technical Report 110, LSTA, Univ. Paris VI, Paris.Google Scholar
- Diebolt, J. and Robert, C. (1990b). Bayesian estimation of finite mixture distributions, part II: Sampling implementation. Technical Report 111, LSTA, Univ. Paris VI, Paris.Google Scholar
- MacLachlan, G. and Basford, K. (1988). Mixture Models: Inference and Applications to Clustering. Marcel Dekker, New York.Google Scholar
- Guillin, A., Marin, J., and Robert, C. (2004). Estimation bayésienne approximative par échantillonnage préférentiel. Revue Statist. Appliquée. (to appear).Google Scholar
- Seher, G. (1992). A review of estimating animal abundance (ii). Workshop on Design of Longitudinal Studies and Analysis of Repeated Measure Data, 60: 129–166.Google Scholar
- Lehmann, E. (1998). Introduction to Large-Sample Theory. Springer-Verlag, New York.Google Scholar