The Inference of Physical Phenomena in Chemistry: Abstract Tomography, Gedanken Experiments, and Surprisal Analysis

Abstract

The maximum entropy method for tomographic reconstruction of a joint probability distribution from its marginals can be applied to problems frequently encountered in molecular dynamics. Once obtained the posterior joint probability can be used to predict the outcomes of untested gedanken experiments. These predictions can often be more readily assimilated than the raw data itself, allowing the scientist to tap his or her intuition further. Surprisal analysis of the gedanken measurements can reveal how many hidden constraints are active in the experimental process. Two problems often face the experimentalist: first, it may be infeasible to directly measure a quantity of interest although various projections of it can be sampled. Second, the sheer complexity of multidimensional projection data prohibits an intuitive grasp of the data’s scientific content. We recommend breaking the analysis into three parts: tomographic back-projection to manage the data, gedanken experiment prediction to stimulate discovery of unused prior information, and surprisal analysis for discovery of hidden constraints. Two new methods of applying graphical surprisal analysis to multidimensional data are described. Example applications to five molecules are given.