Bayesian model comparison with un-normalised likelihoods

Everitt, R. G., Johansen, A. M., Rowing, E. and Evdemon-Hogan, M. (2017) Bayesian model comparison with un-normalised likelihoods. Statistics and Computing, 27 (2). pp. 403-422. ISSN 1573-1375 doi: 10.1007/s11222-016-9629-2

Abstract/Summary

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalizing constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to the intractability of their likelihood functions. Several methods that permit exact, or close to exact, simulation from the posterior distribution have recently been developed. However, estimating the evidence and Bayes’ factors for these models remains challenging in general. This paper describes new random weight importance sampling and sequential Monte Carlo methods for estimating BFs that use simulation to circumvent the evaluation of the intractable likelihood, and compares them to existing methods. In some cases we observe an advantage in the use of biased weight estimates. An initial investigation into the theoretical and empirical properties of this class of methods is presented. Some support for the use of biased estimates is presented, but we advocate caution in the use of such estimates.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/54861
Identification Number/DOI	10.1007/s11222-016-9629-2
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics > Applied Statistics
Publisher	Springer
Download/View statistics	View download statistics for this item