Bayesian inference and computation for confounding adjustment and causation

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Most statistical analysis procedures that attempt to uncover the relationship between influential factors (for example, exposure to hazardous materials in the environment, medical treatment or economic intervention) and response (eg health or socio-economic outcome) are prone to problems if the statistical models used are incorrectly specified. In particular, if there are factors that influence both exposure and response, then statistical inferences must be carefully drawn. In many situations, particularly when the number of potential influential factors or predictors is large, it is extremely difficult to ensure correct model specification, and this represents a considerable methodological and analytic challenge. My proposed research is in the domain of causal inference, that attempts to quantify the true effect of exposure on response when the number of potential influential factors is large. In particular, I will use the Bayesian framework that allows for a more complete analysis of the variability and uncertainty associated with the analysis. There are significant mathematical theory, and methodological, challenges in this area, but once the necessary theory and methods are established, the proposed work has the potential to influence statistical practice, and thereby aid in the quantitative analysis of data in a wide range of scientific and other research domains. It is widely recognized that correct statistical analysis is a vital component of most research pursuits. The goal of the proposed research is to add to the statistical tools available to researchers. In the next five years; my short term goals address specific methodological challenges that are the focus of much interest in this domain; forming a correct framework for statistical inference, performing model selection, and reducing variability and increasing stability of existing procedures. The resulting developments will help to solve real, practical problems in the statistical analysis of data. In the longer term, I will address some remaining methodological and theoretical issues concerned with extending the current framework.