Spatio-temporal models for mapping the incidence of malaria in Pará

Our main aims in this article are: (i) to model the means by which rainfall affects malaria incidence in the state of Pará, one of Brazil's largest states; and (ii) to check for similarities along the counties in the state. We use state of the art spatial-temporal models which can, we believe, anticipate various kinds of interactions and relations that might be present in the data. We use the traditional Poisson-normal model where, at any given time, the incidences of malaria for any two counties are conditionally independent and Poisson distributed with log-mean explained by rainfall and random effects terms. Our methodological contribution is in allowing some of the random effects variances to evolve with time according to a dynamic model. Additionally, the change of support problem caused by combining malaria counts (per county) with rainfall (per station) is partially solved by interpolating the whole state through a Gaussian process. Posterior inference and model comparison are computationally assessed via Markov chain Monte Carlo (MCMC) methods and deviance information criteria (DIC), respectively.