Bayesian inference for nonlinear multivariate diffusion processes, with application to biochemical network dynamics

 

Biochemical network dynamics follow a continuous-time discrete-state stochastic process governed by the Chemical Master Equation. It is of considerable practical interest to be able to infer the rate constants that parameterise this process using partial discrete-time observations on the process state. Although it is possible to construct MCMC algorithms that directly solve this problem, they do not scale-up well to problems of interesting size and complexity. It appears more promising to work with an approximation to the real process, known as the Chemical Langevin Equation. Inference for this nonlinear multivariate diffusion process is also a very challenging problem, due to the high dependence between the process parameters and unobserved sample paths. However, in recent years there have been a number of interesting developments in the area of inference for diffusions that are relevant to this problem. I will present a new approach to the solution of the problem that utilises MCMC, sequential filtering, and a multivariate variant of the modified diffusion-bridge construct of Durham and Gallant. The technique will be illustrated in the context of some biochemical network problems.