A study of the data augmentation strategy for stochastic differential equations. Issue 10 (2nd July 2020) - Liu, Ge; Craigmile, Peter F.; Herbei, Radu
ABSTRACT: Multivariate stochastic differential equations (SDEs) are commonly used in many applications. Statistical inference based on discretely observed data requires estimating the transition density, which is unknown for most models. Typically, one would estimate the transition density and use the approximation for statistical inference. However, many estimation methods will fail when the observations are too sparse or when the SDE models have a hierarchical structure. In a Bayesian approach, we explore the posterior distribution of the SDE model parameters. In the Markov Chain Monte Carlo algorithm, we use data augmentation to understand how the approximation of the transition density affects the inference procedure. We give guidelines on balancing the computational demands with the need to provide reliable and accurate posterior inference. Simulations are used to evaluate these guidelines. We demonstrate these methods on the analysis of oceanography tracer measurements.