title: An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations.
abstract: Selection among alternative theoretical models given an observed dataset 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 and 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 Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel 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.
authors.affiliation: Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Department of Physics and Astronomy , Northwestern University , Evanston, IL, USA ; School of Physics and Astronomy, University of Birmingham , Birmingham, UK.
authors.forename: W M
authors.initials: WM
authors.lastname: Farr
authors.affiliation: MIT Kavli Institute , Cambridge, MA, USA ; School of Physics and Astronomy, University of Birmingham , Birmingham, UK ; Monash Center for Astrophysics and School of Physics and Astronomy , Monash University , Clayton, Victoria, Australia.
authors.forename: I
authors.initials: I
authors.lastname: Mandel
authors.affiliation: Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Department of Physics and Astronomy , Northwestern University , Evanston, IL, USA ; Department of Astronomy , The Ohio State University , Columbus, OH, USA.
authors.forename: D
authors.initials: D
authors.lastname: Stevens
keywords: Markov chain Monte Carlo; data analysis; reversible-jump Markov chain Monte Carlo