Inference for SDE models via Approximate Bayesian Computation

TL;DR

This paper develops an efficient Approximate Bayesian Computation (ABC) method for inference in complex stochastic differential equation models, especially in high-dimensional and latent variable contexts, demonstrated through simulations.

Contribution

It introduces a computationally efficient ABC-MCMC algorithm tailored for multidimensional SDE models, reducing runtime significantly compared to existing methods.

Findings

Halves the computational time of ABC-MCMC in simulations

Successfully applied to pharmacokinetics/pharmacodynamics models

Provides a MATLAB package for practical implementation

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 e.g. financial, neuronal and population growth dynamics. However inference for multidimensional SDE models is still very challenging, both computationally and theoretically. 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. A computationally efficient ABC-MCMC algorithm is proposed, halving the running time in our simulations. Focus 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. Simulation studies for a pharmacokinetics/pharmacodynamics model and for stochastic chemical reactions are considered and a MATLAB package implementing our ABC-MCMC algorithm is provided.