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. 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. By exploiting the properties of the considered ABC methods a computationally efficient MCMC algorithm is proposed, halving the running time of our simulations. Focus is on the case where the SDE describes dynamics 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 pharmacokinetic/pharmacodynamic model and for stochastic chemical reactions are considered.
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