Title: Nonparametric Bayesian inference and goodness of fit testing for stochastic differential equations
Authors: Ioanna Manolopoulou - University College London (United Kingdom) [presenting]
Yvo Pokern - University College London (United Kingdom)
Tjun Yee Hoh - University College London (United Kingdom)
Abstract: Methodology is developed for non-parametric Bayesian inference for 2-dimensional diffusion processes, motivated by the study of trajectories in animal movement. We employ an interpretable conjugate Gaussian measure prior whose precision operator is chosen to be a high order differential operator, and construct efficient pseudo-spectral samplers for Markov chain Monte Carlo posterior sampling for the drift, diffusivity and diffusion bridges. Evaluation of model fit for diffusion processes is currently lacking, with many applications of diffusions to real data in the literature suffering obviously poor model fit. We extend an existing transition density-based test to the case of non-parametric drift. We study the finite-sample behaviour of the test statistic and compute Bayesian discrepancy p-values. We illustrate our methods on a dataset following the movement of a Capuchin monkey and describe how outlier removal and systematic sub-sampling of the data can be beneficial to model fit.