Basic statistics and variational concepts behind the reverse Monte Carlo technique

Abstract

We revise the statistical foundations of the reverse Monte Carlo (RMC) technique by constructing the associated functional of a variational principle which incorporates, without any ad hoc assumptions, the inherent errors accompanying the simulation and the experimental data. We propose a Bayesian criteria for acceptance/rejection of configurations, in terms of the variations of the functional. The loss function and variational functional minimization approaches are compared.

Keywords:

• Statistical mechanics
• Reverse Monte Carlo
• Functional analysis
• Loss function

Acknowledgements

We thank Drs. Bo Jönsson, T.Åkesson, Bo Svensson and Léo Degrève for stimulating discussions. We also acknowledge the CNPq, FAPESP/Brazil, CDCHT-ULA and FONACIT (G9700741)/Venezuela for the financial support during the development of this work.