Title: Unbiased inference for discretely observed hidden Markov model diffusions,
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.