Inference for SDE Models via Approximate Bayesian Computation

Abstract

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, for example, financial, neuronal, and population growth dynamics. However, inference for multidimensional SDE models is still very challenging, both computationally and theoretically. Approximate Bayesian computation (ABC) allows to perform Bayesian inference for models which are sufficiently complex that the likelihood function is either analytically unavailable or computationally prohibitive to evaluate. A computationally efficient ABC-MCMC algorithm is proposed, halving the running time in our simulations. Focus here is on the case where the SDE describes latent dynamics in state-space models; however, the methodology is not limited to the state-space framework. We consider simulation studies for a pharmacokinetics/pharmacodynamics model and for stochastic chemical reactions and we provide a Matlab package that implements our ABC-MCMC algorithm.

Key Words:

• Early–rejection MCMC
• Likelihood-free inference
• State-space model
• Stochastic chemical reaction
• Stochastic differential equation

ACKNOWLEDGMENTS

This work has been partially supported by the Faculty of Science at Lund University under the grant “Money Tools” (verktygspengar). The author wishes to acknowledge the comments provided by an Associate Editor and two reviewers which improved the quality of this work considerably.