Journal
STATISTICS AND COMPUTING
Volume 21, Issue 4, Pages 649-656Publisher
SPRINGER
DOI: 10.1007/s11222-010-9198-8
Keywords
Nested sampling; Bayesian computation; Markov chain Monte Carlo
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We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested probability distributions, each successive distribution occupying similar to e (-1) times the enclosed prior mass of the previous distribution. While NS technically requires independent generation of particles, Markov Chain Monte Carlo (MCMC) exploration fits naturally into this technique. We illustrate the new method on a test problem and find that it can achieve four times the accuracy of classic MCMC-based Nested Sampling, for the same computational effort; equivalent to a factor of 16 speedup. An additional benefit is that more samples and a more accurate evidence value can be obtained simply by continuing the run for longer, as in standard MCMC.
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