Inference for SDE models via Approximate Bayesian Computation

Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard tool to model e.g. financial, neuronal and population growth dynamics. However inference for multidimensional SDE models is still very challenging from a computational and theoretical point of view. Recent advances in Approximate Bayesian Computation (ABC) allow to perform Bayesian inference for models which are sufficiently complex that the likelihood function is either analytically unavailable or computationally prohibitive to evaluate. We want to consider how Bayesian inference can be effectively applied to complex SDE models via an MCMC ABC algorithm. Focus is on the case where the SDE describes the dynamics of observations which are affected by measurement error, the latter being a non-negligible source of variability (and inferential complications) for most biomedical/biostatistical applications. Simulation studies for a simple pharmacokinetic model and a more complex multidimensional SDE for the modellization of stochastic kinetic networks are considered.