  Variants of fluctuation theorems recently discovered in the statistical
mechanics of non-equilibrium 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 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. We also discuss the determination of averages over
multimodal posterior distributions with the help of a variant of the Crooks
theorem. All our findings are verified by extensive numerical simulations of
two model systems with bimodal likelihoods.
