Accelerating inference for diffusions observed with measurement error and large sample sizes using Approximate Bayesian Computation

In recent years statistical inference has been provided with a range of breakthrough methods to perform exact Bayesian inference for dynamical models. However it is often not feasible to apply exact methodologies in the context of large datasets and complex models. This paper consider a nonlinear stochastic differential equation model observed with correlated measurement errors and an application to a protein folding problem. An Approximate Bayesian Computation (ABC) MCMC algorithm is suggested to allow inference for model parameters within reasonable time constraints. The ABC algorithm uses simulations of subsamples as well as a so-called "early rejection" strategy to speed up computations in the ABC-MCMC sampler. A small sample simulation study is conducted to compare our strategy with exact Bayesian inference, the latter resulting two orders of magnitude slower than ABC-MCMC for the considered setup. Finally the ABC algorithm is applied to a large size protein data. The suggested methodology is fairly general and not limited to the exemplified model and data.