Novos modelos de vizinhança espacial

Abstract

In the first paper, we introduce the Probabilistic Context Neighborhood model for two dimensional lattices as an extension of the Probabilistic Context Tree model in one dimensional space preserving some of its interesting properties. This model has a variable neighborhood structure with a fixed geometry but varying radius. In this way we are able to compute the cardinality of the set of neighborhoods and use the Pseudo-Likelihood Bayesian Criterion to select an appropriate model given the data. We represent the dependence neighborhood structure as a tree making easier to understand the model complexity. We provide an algorithm to estimate the model that explores the sparse tree structure to improve computational efficiency. We also present an extension of the previous model, the Non-Homogeneous Probabilistic Context Neighborhood model, which allows a spatially changing Probabilistic Context Neighborhood as we move on the lattice. In the second paper, we proposed a Bayesian approach to the problem of choosing the neighborhood matrix in disease mapping. We use the model proposed by Besag et al. (1991), whose random effects follow the Autoregressive Conditional (CAR), using the adjacency matrix as neighborhood. However, the adjacency matrix is inadequate for scenarios in which the spatial structure is insufficient to obtain a precise estimative of the relative risks, as occurs in criminological and epidemiological studies that show high incidence rates in large towns, regardless the rates presented by neighboring cities. In addition to the a priori classes, we proposed two a posteriori estimators for the neighborhood structure. Finally, we presented several examples, simulations and applications of our method, which reached more satisfactory results than the CAR model. In the last paper, we propose a surveillance system to prospectively monitor the emergence of space-time clusters in point pattern of disease events. Its aim is to detect a cluster as soon as possible after its emergence and it is also desired to keep the rate of false alarms at a controlled level. It is an easily understood and easily implemented system, requiring very little input from the user. This makes it a promising candidate to practical use by public health official agencies. Our method is a modification from a previous proposal made by Rogerson, who examined a retrospective surveillance scenario, looking for the earliest time in the past that change could have been deemed to occur. We modify his method to take into account the prospective case. We evaluated our surveillance system in several scenarios, including without and with emerging clusters, checking distributional assumptions and assessing performance impacts of different emergence times, shapes, extent and intensity of the emerging clusters.