Diffusive nested sampling

• DOI: 10.1007/s11222-010-9198-8
• Publication Date: 2010-08-24T21:08:38Z
• Authors: Brendon J. Brewer; Livia B. Pártay; Gábor Csányi
• Keywords: Statistics and Probability; Computational Theory and Mathematics; Physics - Data Analysis, Statistics and Probability; 0103 physical sciences; Statistics, Probability and Uncertainty; Astrophysics - Instrumentation and Methods for Astrophysics; Statistics - Computation; 01 natural sciences; Theoretical Computer Science

Comment: Accepted for publication in Statistics and Computing. C++ code available at http://lindor.physics.ucsb.edu/DNest<br/>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. 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.<br/>