  State-space models (SSMs) are commonly used to model time series data where
the observations depend on an unobserved latent process. However, inference on
the model parameters of an SSM can be challenging, especially when the
likelihood of the data given the parameters is not available in closed-form.
One approach is to jointly sample the latent states and model parameters via
Markov chain Monte Carlo (MCMC) and/or sequential Monte Carlo approximation.
These methods can be inefficient, mixing poorly when there are many highly
correlated latent states or parameters, or when there is a high rate of sample
impoverishment in the sequential Monte Carlo approximations. We propose a novel
block proposal distribution for Metropolis-within-Gibbs sampling on the joint
latent state and parameter space. The proposal distribution is informed by a
deterministic hidden Markov model (HMM), defined such that the usual
theoretical guarantees of MCMC algorithms apply. We discuss how the HMMs are
constructed, the generality of the approach arising from the tuning parameters,
and how these tuning parameters can be chosen efficiently in practice. We
demonstrate that the proposed algorithm using HMM approximations provides an
efficient alternative method for fitting state-space models, even for those
that exhibit near-chaotic behavior.
