"Local-EM, spatial-temporal modelling and mismeasured data"

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Data that are incomplete may be interval censored, may have arisen in a panel study or may be spatial-temporal in nature. For example, studying the environmental determinants of a rare disease may involve census data collected periodically over decades and across an expansive geographic region. Such data is aggregated in both space and time, and can be complicated by the fact that the spatial aggregation is time dependent as census boundaries change to reflect urban growth and its impact on rural regions. Examples includes a study of Lupus in the Greater Toronto Area and the incidence of mesothelioma in Lambton and Middlesex counties in the Province of Ontario. This project aims to develop spatial-temporal methods for such incomplete data. The methods will be flexible and computationally intensive. The central device is a local likelihood whose use in the context of incomplete data leads naturally to the development of local-EM algorithms. Fan, Stafford and Brown (2011) embed this class of algorithms in a broader context by exposing its relationship to the EMS algorithm and hence a larger class of penalized likelihoods. The advantages of this, which are to be explored, is that it permits avenues of study for local-EM algorithms and resulting estimators. This includes the development of theoretic and inferential properties, the extension of methods to spatial-temporal contexts common in epidemiological studies, and the incorporation of mismeasured data. The latter will place at least some of this research in a context that lies at the interface of structural models for missing data and functional models for data observed with measurement error. Finally, the methods to be developed are computationally intensive but can implemented using multiple processors. Consequently they exploit modern trends in parallel computing that are dramatically increasing computational power. By having the advantage of being amenable to parallel computing the methods outperform alternative MCMC implementations. Computations will be performed on the General Purpose Cluster supercomputer at the SciNet HPC Consortium.