Title: Statistical Computation for Problems in Dynamic Systems and Protein Folding
Description: Inference for dynamic systems and conformational sampling for protein folding are two problems motivated by applied data, which pose computational challenges from a statistical perspective. Dynamic systems are often described by a set of coupled differential equations, and methods of parametric estimation for these models from noisy data can require repeatedly solving the equations numerically. Many of these models also lead to rough likelihood surfaces, which makes sampling difficult. We introduce a method for Bayesian inference on these models, using a multiple chain framework that exploits the underlying mathematical structure and interpolates the posterior to improve efficiency. In protein folding, a large conformational space must be searched for low energy states, where any energy function constructed on the states is at best approximate. We propose a method for sampling fragment conformations that accounts for geometric and energetic constraints, and explore ideas for folding entire proteins that account for uncertain energy landscapes and learning from data more effectively. These ingredients are combined into a framework for tackling the problem of generating improvements to protein structure predictions.