  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 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.
