An Efficient Interpolation Technique for Jump Proposals in Reversible-Jump Markov Chain Monte Carlo Calculations

Details An Efficient Interpolation Technique for Jump Proposals in Reversible-Jump Markov Chain Monte Carlo Calculations An Efficient Interpolation Technique for Jump Proposals in Reversible-Jump Markov Chain Monte Carlo Calculations

2011-04-06

arxiv.org/abs/1104.0984v1

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

8 pages, 2 figures; submitted to Physical Review D

Scientific paper

Selection among alternative theoretical models given an observed data set is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty: it requires jumps between model parameter spaces, but cannot retain a memory of the favored locations in more than one parameter space at a time. Thus, a naive jump between parameter spaces is unlikely to be accepted in the MCMC algorithm and convergence is correspondingly slow. Here we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose inter-model jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in arbitrary dimensions. We show that our technique leads to dramatically improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also discuss the use of the same interpolation technique in two other contexts: as a convergence test for a single-model MCMC and as a way to construct efficient "global" proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution.

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