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Theory and Methods

Sampling-Based Approaches to Calculating Marginal Densities

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Pages 398-409 | Received 01 Nov 1988, Published online: 28 Feb 2012
 

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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