Simulation of and inference stochastic non-linear dynamical systems, frequently studied in systems biology, has historically been too slow to enable parameter inference for all but the simplest systems. In order to calculate the probability distributions associated with these models, approximations to the likelihoods are frequently necessary, but these come with associated drawbacks in accuracy. Recent advances in both stochastic simulation algorithms and efficient Bayesian parameter estimation methodology enable much larger systems, such as those found in cell signalling and circadian clock applications, to be analysed and their parameters inferred. Sensitivity of the model outputs is also highlighted as an important step in the inferential process.
In this talk, I will propose a new method that enables fast exact Bayesian inference using an approximation to the underlying stochastic dynamics, which maintains long-term accuracy of the underling oscillatory systems. The proposed method is applied to several high-dimensional oscillatory systems, with up to 12 variables and 40 parameters, across extensive simulation studies.