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

TL;DR

This paper introduces an adaptive interpolation technique using kD-trees to improve jump proposals in reversible-jump MCMC, enhancing convergence in Bayesian model selection tasks across physics and astronomy.

Contribution

The authors develop a novel interpolation method based on kD-trees that accelerates convergence of RJMCMC by efficiently proposing inter-model jumps using single-model MCMC samples.

Findings

Improved convergence in RJMCMC with the interpolation technique.

Demonstrated efficiency of the method in modest dimensional spaces.

Applicable to constructing global proposals for single-model MCMCs.

Abstract

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 efficiently explore both parameter spaces at once. 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 modest dimensionality. We show that our technique leads to 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 demonstrate the use of the same interpolation technique as a way to construct efficient "global" proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher-dimensional spaces efficiently.