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Diffusive nested sampling

Abstract

We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising con- stant. The method uses one or more particles, which explore a mixture of nested probability distributions, each succes- sive distribution occupying ∼ e−1 times the enclosed prior mass of the previous distribution. While NS technically re- quires 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 clas- sic MCMC-based Nested Sampling, for the same computa- tional effort; equivalent to a factor of 16 speedup. An ad- ditional 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.

Author

Brendon J. Brewer · Livia B. Pártay · Gábor Csányi

Journal

Statistics & Computing

Paper Publication Date

2011

Paper Type

Astroinformatics

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