Title: Verifiable posterior consistency conditions for jump diffusions
Authors: Jere Koskela - University of Warwick (United Kingdom) [presenting]
Dario Spano - University of Warwick (United Kingdom)
Paul Jenkins - University of Warwick (United Kingdom)
Abstract: Jump diffusions are a flexible class of stochastic models for time series data, with abundant applications in a variety of fields. They are natural to specify in terms of function- and measure-valued coefficients, which motivates the use of nonparametric inference methods which are able to retain this level of modelling flexibility. However, likelihoods under jump diffusions are almost always intractable, which makes the development and analysis of methods challenging. We will introduce jump diffusions, as well as the machinery of Bayesian nonparametric inference for discretely observed jump diffusion trajectories. We will then present tractable sufficient conditions on the prior for posterior consistency, and examples of standard nonparametric priors which satisfy the consistency conditions.