Exploring Markovian Projection to Accelerate Pseudo-Marginal Parameter Inference of Biochemical Systems

Supervisor: Dr David J. Warne

A key step in the inverse problem for complex stochastic biochemical reaction networks is the statistical estimation of kinetic rate parameters. Existing theory in this area often focuses on inference based on a full model with normal random error to reflect real-life observational conditions. In practice, only a small subset of chemical species are observable due to limitations in observational processes. As a result, the likelihood function does not have a closed form, and particle filters are required to estimate the likelihood using Monte Carlo. Markovian projection is a novel approach that enables the dimensionality of the biochemical network to be reduced to the number of  observable states only. In this project, we explored the potential for Markovian projection to accelerate bootstrap particle filters used for pseudo-marginal methods for Bayesian inference of kinetic rate parameters. Using a stochastic model of enzyme kinematics as an example, we demonstrate computational speedup for both exact and approximate stochastic simulation schemes for the projected model. We also demonstrate a reduction in the variance of the particle filter likelihood estimator. This highlights the potential for improvements in pseudo-marginal inference using Markov Chain Monte Carlo (MCMC). While we note some basis in likelihood estimates due to the Markovian projection procedure, we show empirically that this bias is almost constant and will not affect the target distribution. We conclude that further research should be conducted to adapt Markovian projection methods into pseudo-marginal MCMC schemes.