Statistical Framework for Uncertainty Quantification in Computational Molecular Modeling

Computational molecular modeling often involves noisy data including uncertainties in model parameters, computational approximations etc., all of which propagates to uncertainties in all computed quantities of interest (QOI). This is a fundamental problem that is often left ignored or treated without sufficient rigor. In this article, we introduce a statistical framework for modeling such uncertainties and providing certificates of accuracy for several QOI. Our framework treats sources of uncertainty as random variables with known distributions, and provides both a theoretical and an empirical technique for propagating those uncertainties to the QOI, also modeled as a random variable. Moreover, the framework also enables one to model uncertainties in a multi-step pipeline, where the outcome of one step cascades into the next. While there are many sources of uncertainty, in this article we have applied our framework to only positional uncertainties of atoms in high resolution models, and in the form of B-factors and their effect in computed molecular properties. The empirical approach requires sufficiently sampling over the joint space of the random variables. We show that using novel pseudo-random number generation techniques, it is possible to achieve the required coverage using very few samples. We have also developed intuitive visualization models to analyze uncertainties at different stages of molecular modeling. We strongly believe this framework would be immensely valuable in evaluating predicted computational models, and provide statistical guarantees on their accuracy.