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Unbiased inference for discretely observed hidden Markov model diffusions

26 July 2018
Neil K. Chada
Jordan Franks
Ajay Jasra
K. Law
ArXiv (abs)PDFHTML
Abstract

We develop an importance sampling (IS) type estimator for Bayesian joint inference on the model parameters and latent states of a class of hidden Markov models. The hidden state dynamics is a diffusion process and noisy observations are obtained at discrete points in time. We suppose that the diffusion dynamics can not be simulated exactly and hence one must time-discretise the diffusion. Our approach is based on particle marginal Metropolis--Hastings, particle filters, and multilevel Monte Carlo. The resulting IS type estimator leads to inference without a bias from the time-discretisation. We give convergence results and recommend allocations for algorithm inputs. In contrast to existing unbiased methods requiring strong conditions on the diffusion and tailored solutions, our method relies on standard Euler approximations of the diffusion. Our method is parallelisable, and can be computationally efficient. The user-friendly approach is illustrated with two examples.

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