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

In recent years statistical inference has been provided with a range of breakthrough methods to perform exact (Bayesian) inference for dynamical models. However in some cases it is challenging to apply exact methodologies with large datasets and increasingly complex models. Here we propose a strategy to allow Bayesian inference to be applied on a relatively large dataset where dynamics are expressed as a sum of diffusions, using Approximate Bayesian Computation (ABC). A new model for protein folding data is proposed for a case study where inference on data is conducted via ABC. Then a simulation study is considered for comparing ABC with exact Bayesian inference. The methodology is fairly general and not limited to models expressed as sums of diffusions.