MCMC Techniques for Parameter Estimation of ODE Based Models in Systems Biology

Abstract

Ordinary differential equation systems (ODEs) are frequently used for dynamical system modelling in many science fields such as economics, physics, engineering, and systems biology. A special challenge in systems biology is that ODE systems typically contain kinetic rate parameters, which are unknown and have to be estimated from data. However, non-linearity of ODE systems together with noise in the data raise severe identifiability issues. Hence, Markov Chain Monte Carlo (MCMC) approaches have been frequently used to estimate posterior distributions of rate parameters. However, designing a good MCMC sampler for high dimensional and multi-modal parameter distributions remains a challenging task. Here we performed a systematic comparison of different MCMC techniques for this purpose using five public domain models. The comparison included Metropolis-Hastings, parallel tempering MCMC, adaptive MCMC and parallel adaptive MCMC. In conclusion, we found specifically parallel adaptive MCMC to produce superior parameter estimates while benefitting from inclusion of our suggested informative Bayesian priors for rate parameters and noise variance.