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Sampling-based approaches to calculating marginal densities. (English) Zbl 0702.62020
Summary: 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.

MSC:
62E99 Statistical distribution theory
65C99 Probabilistic methods, stochastic differential equations
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