Favaro, alberto and Nickelsen, Daniel and Barykina, Elena and Engel, Andreas (2015) Prior-predictive value from fast-growth simulations: Error analysis and bias estimation. Physical Review E, 91. 012127. ISSN 1550-2376

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Abstract

Variants of fluctuation theorems recently discovered in the statistical mechanics of nonequilibrium processes may be used for the efficient determination of high-dimensional integrals as typically occurring in Bayesian data analysis. In particular for multimodal distributions, Monte Carlo procedures not relying on perfect equilibration are advantageous. We provide a comprehensive statistical error analysis for the determination of the prior-predictive value (the evidence) in a Bayes problem, building on a variant of the Jarzynski equation. Special care is devoted to the characterization of the bias intrinsic to the method and statistical errors arising from exponential averages. We also discuss the determination of averages over multimodal posterior distributions with the help of a consequence of the Crooks relation. All our findings are verified by extensive numerical simulations of two model systems with bimodal likelihoods.

Item Type:	Article
Subjects:	Science and mathematics > Physics
Divisions:	Faculty of Mathematics and Science > Institute of Physics (IfP)
Date Deposited:	19 Mar 2015 10:38
Last Modified:	19 Mar 2015 10:38
URI:	https://oops.uni-oldenburg.de/id/eprint/2196
URN:	urn:nbn:de:gbv:715-oops-22774
DOI:	doi:10.1103/PhysRevE.91.012127
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