Jordan Franks

Unbiased inference for discretely observed hidden Markov model diffusions

Diffusion processes observed with noise in the real world represent
challenging models for Bayesian parameter inference in the presence of
non-linearity, non-Gaussianity, and multi-dimensionality. We propose a
general inference approach for diffusion processes observed with noise,
thus opening up the possibility of inference for such challenging
models. The algorithm is based on a clever combination of popular
algorithms, such as pseudo-marginal and adaptive Markov chain Monte
Carlo, Euler-Maruyama discretisations, particle filters and coupling,
and multi-level Monte Carlo. The algorithm is therefore generally
programmable, and we give a small set of conditions under which the
approach is guaranteed to deliver unbiased model inference. We also
consider the efficiency of the approach within the multi-level
framework. We then apply our algorithm on some example models. This
talk is based on joint work with Ajay Jasra, Kody J.H. Law and Matti Vihola.

Authors:
Jordan Franks, Ajay Jasra, Kody J.H. Law and Matti Vihola

Presenter:
Jordan Franks

Affiliation:
Newcastle University

Email:
jordan.franks@newcastle.ac.uk