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2009

Diffusive Nested Sampling

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

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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 ~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.

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Built on

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Wang, F. and Landau, D. P., Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States, Phys Rev Letters 86, 2050 (2001)
Original
2001
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Neal, R. M., Slice sampling (with discussion), Annals of Statistics, vol. 31, pp. 705-767 (2003)
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Mukherjee, P., Parkinson, D., Liddle, A. R. A Nested Sampling Algorithm for Cosmological Model Selection. The Astrophysical Journal 638, L51-L54 (2006)
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