An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations

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 d...

Full description

Bibliographic Details
Main Authors: W. M. Farr, I. Mandel, D. Stevens
Format: Article
Language:English
Published: The Royal Society 2015-01-01
Series:Royal Society Open Science
Subjects:
Online Access:https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.150030
id doaj-bdb3642e7aab4eaa97b9596f378aef4d
record_format Article
spelling doaj-bdb3642e7aab4eaa97b9596f378aef4d2020-11-25T03:56:27ZengThe Royal SocietyRoyal Society Open Science2054-57032015-01-012610.1098/rsos.150030150030An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculationsW. M. FarrI. MandelD. StevensSelection 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.https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.150030markov chain monte carloreversible-jump markov chain monte carlodata analysis
collection DOAJ
language English
format Article
sources DOAJ
author W. M. Farr
I. Mandel
D. Stevens
spellingShingle W. M. Farr
I. Mandel
D. Stevens
An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations
Royal Society Open Science
markov chain monte carlo
reversible-jump markov chain monte carlo
data analysis
author_facet W. M. Farr
I. Mandel
D. Stevens
author_sort W. M. Farr
title An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations
title_short An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations
title_full An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations
title_fullStr An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations
title_full_unstemmed An efficient interpolation technique for jump proposals in reversible-jump Markov chain Monte Carlo calculations
title_sort efficient interpolation technique for jump proposals in reversible-jump markov chain monte carlo calculations
publisher The Royal Society
series Royal Society Open Science
issn 2054-5703
publishDate 2015-01-01
description 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.
topic markov chain monte carlo
reversible-jump markov chain monte carlo
data analysis
url https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.150030
work_keys_str_mv AT wmfarr anefficientinterpolationtechniqueforjumpproposalsinreversiblejumpmarkovchainmontecarlocalculations
AT imandel anefficientinterpolationtechniqueforjumpproposalsinreversiblejumpmarkovchainmontecarlocalculations
AT dstevens anefficientinterpolationtechniqueforjumpproposalsinreversiblejumpmarkovchainmontecarlocalculations
AT wmfarr efficientinterpolationtechniqueforjumpproposalsinreversiblejumpmarkovchainmontecarlocalculations
AT imandel efficientinterpolationtechniqueforjumpproposalsinreversiblejumpmarkovchainmontecarlocalculations
AT dstevens efficientinterpolationtechniqueforjumpproposalsinreversiblejumpmarkovchainmontecarlocalculations
_version_ 1724464993351499776