Bayesian Computational Methods
The bayesian (or integrated likelihood) approach to statistical modelling and analysis proceeds by representing all uncertainties in the form of probability distributions. Learning from new data is accomplished by application of Bayes's Theorem, the latter providing a joint probability descript...
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Published in | Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 337; no. 1647; p. 369 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
The Royal Society
15.12.1991
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Online Access | Get full text |
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Summary: | The bayesian (or integrated likelihood) approach to statistical modelling and analysis proceeds by representing all uncertainties
in the form of probability distributions. Learning from new data is accomplished by application of Bayes's Theorem, the latter
providing a joint probability description of uncertainty for all model unknowns. To pass from this joint probability distribution
to a collection of marginal summary inferences for specified interesting individual (or subsets of) unknowns, requires appropriate
integration of the joint distribution. In all but simple stylized problems, these (typically high-dimensional) integrations
will have to be performed numerically. This need for efficient simultaneous calculation of potentially many numerical integrals
poses novel computational problems. Developments over the past decade are reviewed, including adaptive quadrature, adaptive
Monte Carlo, and a variant of a Markov chain simulation procedure known as the Gibbs sampler. |
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ISSN: | 1364-503X 1471-2962 |
DOI: | 10.1098/rsta.1991.0130 |