Applying Bayesian Inference to Measurements of Colloidal Dynamics

Abstract

A generative model provides a framework for applying Bayesian methods to complex experimental data like microscope images by describing them as a statistical probability distribution. One of the most valuable features of a Bayesian approach is the ability to marginalize (or average) over parameters that are unknown but of little interest to the task at hand. In this thesis, I emphasize how Bayesian methods, and marginalization in particular, enable sophisticated analysis of experimental results. One experimental technique to study colloids is digital holographic microscopy. A generative model of hologram data must capture the full image formation process, which is complicated but similar across many different types of experiments. To facilitate these efforts, I introduce HoloPy, a versatile code package that defines generative models for experimental hologram images. Focusing on my particular use case, I derive a set of generative models to describe the dynamics of colloidal clusters, or Markov state models more generally, independent of experimental measurement techniques. In the second half of this thesis, I apply the computational and theoretical tools introduced in the first half to experimental data. Specifically, I use a two-dimensional colloidal model to investigate macromolecular folding in a barrierless limit, which is difficult to access with other systems. By using HoloPy and generative models of cluster dynamics, I show that folding proceeds via multiple pathways with competition between the fastest pathways and those that are most frequent. I also show that hydrodynamic interactions are crucial to understanding folding dynamics and must be handled carefully in simulations. Finally, I adapt the experimental system to three dimensions, where preliminary results suggest both similarities and differences as compared to two-dimensional folding.