Prior-predictive value from fast-growth simulations: Error analysis and bias estimation

摘要

Variants of fluctuation theorems recently discovered in the statisticalmechanics of non-equilibrium processes may be used for the efficientdetermination of high-dimensional integrals as typically occurring in Bayesiandata analysis. In particular for multimodal distributions, Monte-Carloprocedures not relying on perfect equilibration are advantageous. We provide acomprehensive statistical error analysis for the determination of theprior-predictive value in a Bayes problem building on a variant of theJarzynski equation. Special care is devoted to the characterization of the biasintrinsic to the method. We also discuss the determination of averages overmultimodal posterior distributions with the help of a variant of the Crookstheorem. All our findings are verified by extensive numerical simulations oftwo model systems with bimodal likelihoods.