Abstract

This talk is divided into two parts. The first part considers systems of stochastic differential equations (SDEs) that are used to describe how a group of interacting populations evolve over time. These systems are widely used in molecular biology to study the mechanisms of gene regulation, cell signalling and development. They are also used as compartmental models in epidemiology and other fields. After a crash course on the topic, I will introduce an SDE model that speeds up standard methods for stochastic simulation while maintaining model accuracy. We will then discuss Bayesian computational methods for estimating the posterior distribution of model parameters using time-series observations, and how the (un)identifiability of model parameters affect estimation. The second part of the talk considers a large-p-small-n dataset of gene expression. In particular, we will discuss the analysis of an atypical single-cell RNA sequencing dataset. This experiment attempts to study the response of single cells to a set of stress factors. We will discuss the use of supervised classification and information theoretic quantities to measure the predictive power of single cells to identify the stress factor based on the expression of their genes. We will also discuss methods for comparing the importance of features involved in those responses. Finally, we will discuss an attempt to learn the decision-making logic of cells when responding to multi-component, nested stress factors.