Rao-Blackwellized particle mcmc for parameter estimation in spatio-temporal Gaussian processes

In this paper, we consider parameter estimation in latent, spatiotemporal Gaussian processes using particle Markov chain Monte Carlo methods. In particular, we use spectral decomposition of the covariance function to obtain a high-dimensional state-space representation of the Gaussian processes, which is assumed to be observed through a nonlinear non-Gaussian likelihood. We develop a Rao-Blackwellized particle Gibbs sampler to sample the state trajectory and show how to sample the hyperparameters and possible parameters in the likelihood. The proposed method is evaluated on a spatio-temporal population model and the predictive performance is evaluated using leave-one-out cross-validation.