Modeling Misaligned Spatio-Temporal Data
Alexandra M. Schmidt, Alexandre S. Silva, Paulo J. Ribeiro Jr.
Statistical Methods, UFRJ, Rio de Janeiro, RJ, Brazil; Statistical Methods, UFRJ, Rio de Janeiro, RJ, Brazil; UFPR

Our aim is to estimate the abundance of eggs of the mosquito Aedes aegypti, one of the vectors responsible for transmitting dengue fever, over a region of Recife, in the Northeast of Brazil. We have available the abundance of eggs observed at n locations, during T consecutive weeks in Recife.

More specifically, the abundances were observed at n=84 locations from May 2004 until May 2006.

Because of fund limitations, the n locations were divided into K=4 groups, and at each week t, samples were collected only at the locations belonging to group k=1,2,...,K, such that n=n_1+n_2+...n_K, where n_k is the number of locations in group k.

We propose a spatio-temporal model which naturally accounts for the misalignment present in the data and borrows strength among the observed locations, across the different weeks, to learn about the behavior of the abundance of eggs during this period.

The temporal structure is modelled through dynamic linear models and the spatial structure is captured through Gaussian processes.

Inference procedure is based on the Bayesian paradigm, which naturally provides uncertainties about our estimates. The missing observations are estimated through their resultant posterior predictive distributions.

Keywords: Bayesian paradigm; Borrowing strength; Dynamic models; Spatial misalignment

Biography: Alexandra Schmidt is an Associate Professor of the Department of Statistical Methods at the Federal University of Rio de Janeiro, Brazil. Her main areas of research are Bayesian models for spatial and spatio-temporal processes. She has published papers in the JRSS B, Test, Environmetrics, International Statistical Review, among other journals. She is Past-Chair of the Program Council of the International Society for Bayesian Analysis, elected member of ISI, and an associate editor of Environmetrics and The Brazilian Journal of Probability and Statistics.