The Annals of Applied Statistics

A bivariate space–time downscaler under space and time misalignment

Veronica J. Berrocal, Alan E. Gelfand, and David M. Holland

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Ozone and particulate matter, PM2.5, are co-pollutants that have long been associated with increased public health risks. Information on concentration levels for both pollutants comes from two sources: monitoring sites and output from complex numerical models that produce concentration surfaces over large spatial regions. In this paper, we offer a fully-model-based approach for fusing these two sources of information for the pair of co-pollutants which is computationally feasible over large spatial regions and long periods of time. Due to the association between concentration levels of the two environmental contaminants, it is expected that information regarding one will help to improve prediction of the other. Misalignment is an obvious issue since the monitoring networks for the two contaminants only partly intersect and because the collection rate for PM2.5 is typically less frequent than that for ozone.

Extending previous work in Berrocal, Gelfand and Holland (2010), we introduce a bivariate downscaler that provides a flexible class of bivariate space–time assimilation models. We discuss computational issues for model fitting and analyze a dataset for ozone and PM2.5 for the ozone season during year 2002. We show a modest improvement in predictive performance, not surprising in a setting where we can anticipate only a small gain.

Article information

Ann. Appl. Stat., Volume 4, Number 4 (2010), 1942-1975.

First available in Project Euclid: 4 January 2011

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Co-kriging coregionalization dynamic model kriging multivariate spatial process spatially varying coefficients


Berrocal, Veronica J.; Gelfand, Alan E.; Holland, David M. A bivariate space–time downscaler under space and time misalignment. Ann. Appl. Stat. 4 (2010), no. 4, 1942--1975. doi:10.1214/10-AOAS351.

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Supplemental materials

  • Supplementary material: Fitting details. This section provides details for fitting the bivariate downscaler model. In the section we will first illustrate how to fit the general bivariate downscaler model in its static version, and then we will discuss how to adapt the fitting model procedures from the static setting to the space-time setting.