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29 March 2024
 
  » arxiv » 0912.2380

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Diffusive Nested Sampling
Brendon J. Brewer ; Livia B. Pártay ; Gábor Csányi ;
Date 12 Dec 2009
AbstractWe introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses a single particle, which explores a mixture of nested probability distributions, each successive distribution occupying ~ e^{-1} times the enclosed prior mass of the previous distribution. While classic NS technically requires independent generation of particles, imperfect 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 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 waiting for longer (as in standard MCMC). This is in contrast with classic NS for which there is no known procedure for merging separate runs when the exploration is imperfect.
Source arXiv, 0912.2380
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