Prior-predictive value from fast-growth simulations: error analysis and bias estimation.
Phys Rev E Stat Nonlin Soft Matter Phys
; 91(1): 012127, 2015 Jan.
Article
in En
| MEDLINE
| ID: mdl-25679590
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.
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Collection:
01-internacional
Database:
MEDLINE
Type of study:
Prognostic_studies
/
Risk_factors_studies
Language:
En
Journal:
Phys Rev E Stat Nonlin Soft Matter Phys
Journal subject:
BIOFISICA
/
FISIOLOGIA
Year:
2015
Document type:
Article
Affiliation country: