Estimating Bayes factors via thermodynamic integration and population MCMC

Calderhead, B. and Girolami, M. (2009) Estimating Bayes factors via thermodynamic integration and population MCMC. Computational Statistics and Data Analysis, 53(12), pp. 4028-4045. (doi: 10.1016/j.csda.2009.07.025)

Abstract

A Bayesian approach to model comparison based on the integrated or marginal likelihood is considered, and applications to linear regression models and nonlinear ordinary differential equation (ODE) models are used as the setting in which to elucidate and further develop existing statistical methodology. The focus is on two methods of marginal likelihood estimation. First, a statistical failure of the widely employed Posterior Harmonic Mean estimator is highlighted. It is demonstrated that there is a systematic bias capable of significantly skewing Bayes factor estimates, which has not previously been highlighted in the literature. Second, a detailed study of the recently proposed Thermodynamic Integral estimator is presented, which characterises the error associated with its discrete form. An experimental study using analytically tractable linear regression models highlights substantial differences with recently published results regarding optimal discretisation. Finally, with the insights gained, it is demonstrated how Population MCMC and thermodynamic integration methods may be elegantly combined to estimate Bayes factors accurately enough to discriminate between nonlinear models based on systems of ODEs, which has important application in describing the behaviour of complex processes arising in a wide variety of research areas, such as Systems Biology, Computational Ecology and Chemical Engineering. (C) 2009 Elsevier B.V. All rights reserved

• Item Type: Articles
• Keywords: BAYES Bayes factor Bias CHAIN MONTE-CARLO INFERENCE LIKELIHOOD Methods MODEL MODELS REGRESSION REGRESSION-MODELS RESEARCH SYSTEM
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Calderhead, Mr Ben and Girolami, Prof Mark
• Authors: Calderhead, B., and Girolami, M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Computational Statistics and Data Analysis
• Publisher: Elsevier
• ISSN: 0167-9473
• First Published: First published in Computational Statistics and Data Analysis 53(12):4028-4045
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher