An infinite-dimensional MCMC for exact Bayesian inference in jump-diffusion processes
Flávio B. Gonçalves (UFMG)

Jump-diffusions have considerable appeal as flexible families of stochastic models. Making statistical inference based on discrete observations of such processes is a complex and challenging problem. Its infinite-dimensional nature has required from existing inference methodologies the use of discrete approximations that naturally represent a considerable source of error. In this talk, we rely on a novel algorithm to perform exact simulation of jump-diffusions bridges as the basis to develop an MCMC algorithm to make inference for jump-diffusion processes. The resulting infinite-dimensional Markov chain has the exact posterior distribution of the parameters and missing paths as its invariant distribution. More specifically, it is a Gibbs Sampling with Barker's steps. The methodology is exact in the sense that it is free of discretisation error and Monte Carlo error is the only source of inaccuracy. The exactness feature is related to the simulation of events of unknown probability. A simulated example is presented to illustrate the methodology.