UC Santa Barbara

Significant modern advances in faster and cheaper measurement techniques for biological processes has led to an explosion in the availability of biological data, from the clinical scale down to the molecular scale with the promise to vastly increase our understanding of these complex systems. However, a critical step in accomplishing this is developing flexible data-driven and statistical methods to make sense of these rich datasets. As measurements in this domain are frequently noisy and sparse, Bayesian methods are promising for providing not only accurate estimates that capture prior knowledge, but also uncertainties in drawing conclusions.

In this thesis, we describe our contributions to the analysis and development of biochemical reaction networks using Bayesian methods, both from applied and computational directions. We begin with an application of a Bayesian model for understanding a biochemical process at the clinical level. Then, we follow by describing our contributions to inferring the parameters and the structure of the biochemical reaction networks from experimental data using Bayesian techniques.

Specifically, we first describe our work in applying a hierarchical Bayesian joint longitudinal survival model to analyze the clinical risks of the protein biomarkers D-Dimer and Factor II, which play a crucial role in the coagulation cascade. Next, we transition to the molecular scale and start by describing our innovations in accelerating a critical step component of the Approximate Bayesian Computation algorithm for Bayesian inference of the parameters of stochastic biochemical reaction networks. Then, we discuss the problem of inferring the structure of biochemical reaction systems from data and describe our contributions to this problem using a Bayesian formulation. We close with our brief work demonstrating the application of stochastic biochemical reaction networks to the field of epidemiology along with some supporting software.

Lastly, we provide summary of our contributions and a few future directions.