Computationally Intensive Methods for Large Spatio-Temporal Data Sets

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***The proposed research concerns data that has been aggregated to fall within a spatial region, an interval of time or both. Such data is increasingly common in large environmental or epidemiological studies. For example, in the instance of a rare disease exploring the spatial structure of disease incidence requires collecting cases over a long period of time often decades. The data usually comes in the form of case counts for subdivisions of a geographic region postal codes or census enumeration areas. If the data is collected periodically, say every five years as in the case of a census, then the data is aggregated in both space and time. One goal of an epidemiological study is to explore the structure of an intensity surface for disease incidence over a geographic region. The objective is to identify any structure that would indicate a higher than expected incidence of disease. Such a “hotspot” may itself be due to an environmental source (e.g. arsenic in ground water affecting the incidence of kidney cancer) or worsening/improving industrial conditions (e.g. the disuse of asbestos on the incidence of mesothelioma). Such aggregated spatio-temporal data has the added complexity that the boundaries of geographic regions can themselves change over time. The result is that over the period of entire study we can't say what the case count is for any subdivision within the study. In addition, the data itself may be mismeasured if, for example, an individuals residential history within the study region varies over time.******The research proposed considers the development of statistical algorithms for the analysis of such messy incomplete data. This includes broadening an existing class of local-EM algorithms to a set of EMS algorithms where the S-step is no longer simply dictated by the choice of kernel in the local likelihood but may now depend on how we model the correlation structure within a hierarchical Bayesian model. Computational efficiency is gained through Gauss Markov random field approximations and sparse matrix computations. Methods rely on modeling the data as a novel root Gaussian Cox process broadening the choice of the square root link function will allow integrated nested Laplace approximations to be extended to aggregated data. All methods proposed will allow for the analysis of data that is known to be mismeasured.**