Grid Based Bayesian Inference for Stochastic Differential Equation Models

This paper introduces a new approach of approximate Bayesian inference for Stochastic Differential Equation (SDE) models. This approach is not MCMC based and aims to provide a more efficient option for Bayesian inference on SDE models. There are two novel aspects about this approach: the first concerns the way in which the parameter space is explored and the second concerns the evaluation of the posterior. We propose two new methods to implement this approach. These methods are the Gaussian Modified Bridge Approximation (GaMBA) and its extension GaMBAImportance sampling (GaMBA-I). This paper provides an easy to use algorithm for both these methods, discusses their consistency properties, describes examples where these methods provide efficient inference and also discusses their limitations.