Sequential Empirical Bayes method for filtering dynamic spatiotemporal processes

TL;DR

This paper introduces a sequential empirical Bayes approach for real-time filtering and parameter estimation of dynamic spatiotemporal processes, utilizing MCMC sampling with novel online updates and a skewed-normal proposal.

Contribution

It presents a new online empirical Bayes method for spatiotemporal data, including a novel online estimation of the spatial range parameter and improved sampling proposals.

Findings

Method performs comparably to offline Bayesian approaches.

Skewed-normal proposal outperforms Gaussian proposals.

Effective application demonstrated in radiation monitoring post-Fukushima.

Abstract

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.