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Sampling-Based Approaches to Calculating Marginal Densities

Alan E. Gelfand and Adrian F. M. Smith
Journal of the American Statistical Association
Vol. 85, No. 410 (Jun., 1990), pp. 398-409
DOI: 10.2307/2289776
Stable URL: http://www.jstor.org/stable/2289776
Page Count: 12
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Sampling-Based Approaches to Calculating Marginal Densities
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Abstract

Stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm can be viewed as three alternative sampling- (or Monte Carlo-) based approaches to the calculation of numerical estimates of marginal probability distributions. The three approaches will be reviewed, compared, and contrasted in relation to various joint probability structures frequently encountered in applications. In particular, the relevance of the approaches to calculating Bayesian posterior densities for a variety of structured models will be discussed and illustrated.

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