Bayesian Sampling of Structural Ensembles: The Role of Ensemble-Counting Measures
This study investigates how different ways of counting structural ensembles affect Bayesian estimates during molecular simulation refinement. It found that the standard flat measure used in the Bayesian Energy Landscape Tilting (BELT) framework creates a non-normalizable posterior distribution for finite simulations. Proposing the Jeffreys measure solves this by providing an invariant counting prescription, ensuring posterior averages are consistent and well-defined.