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Abstract

The Boltzmann distribution is commonly used as a prior probability in Bayesian data analysis. Examples include the Ising model in statistical image analysis and the canonical ensemble based on molecular dynamics force fields in protein structure calculation. These models involve a temperature or weighting factor that needs to be inferred from the data. Bayesian inference stipulates to determine the temperature based on the model evidence. This is challenging because the model evidence, a ratio of two high-dimensional normalization integrals, cannot be calculated analytically. We outline a replica-exchange Monte Carlo scheme that allows us to estimate the model evidence by use of multiple histogram reweighting. The method is illustrated for an Ising model and examples in protein structure determination.