Sequential Empirical Bayes Method for Filtering Dynamic Spatiotemporal Processes

We consider online prediction of a latent dynamic spatiotemporal process
and estimation of the associated model parameters based on noisy data.
The problem is motivated by the analysis of spatial data arriving in
real-time and the current parameter estimates and predictions are updated
using the new data at a fixed computational cost. Estimation and
prediction is performed within an empirical Bayes framework with the aid
of Markov chain Monte Carlo samples. Samples for the latent spatial field
are generated using a sampling importance resampling algorithm with a
skewed-normal proposal and for the temporal parameters using Gibbs
sampling with their full conditionals written in terms of sufficient
quantities which are updated online. The spatial range parameter is
estimated by a novel online implementation of an empirical Bayes method,
called herein \emph{sequential empirical Bayes} method. A simulation
study shows that our method gives similar results as an offline Bayesian
method. We also find that the skewed-normal proposal improves over the
traditional Gaussian proposal. The application of our method is
demonstrated for online monitoring of radiation after the Fukushima
nuclear accident.