Uniform Chi-Squared Model Probabilities in NMR Crystallography

Abstract

A nearly universal component of NMR crystallography is the ranking of candidate structures based on how well their first-principles predicted NMR parameters align with the results of solid-state NMR experiments. Here, a novel approach for assigning probabilities to candidate models is proposed that quantifies the likelihood that each model is the correct experimental structure. This method employs hierarchical Bayesian inference and leverages explicit prior probabilities derived from a uniform distribution of potential candidate structures with respect to chi-squared values. The resulting uniform chi-squared (UC) model provides a more cautious estimate of candidate probabilities compared to previous approaches, assigning decreased likelihood to the best-fit structure and increased likelihood to alternate candidates. Although developed here within the context of NMR crystallography, the UC Model represents a general method for assigning likelihoods based on chi-squared goodness-of-fit assessments.