A Bayesian method for finding interactions

In genomic studies, datasets with a small sample size and a large number of potential predictors are common. Recently, gene-gene interactions (epistasis) and gene-environment interactions have been drawing increasing attention due to the etiology of complex diseases. If all possible pair wise interactions are to be explored, then this leads to a high dimensional model space. There is very little work to handle this common problem.; The emphasis of my research is on selecting interactions and controlling the number of falsely discovered predictors with a limited sample size. The method I propose simultaneously satisfies the two properties for inclusion of interactions: interpretability and discovery. In addition, I develop a novel equivalence between variable selection procedures and the false discovery rate.; One application of my research is the development of a model to aid the therapeutic decision by identifying prognostic factors or interactions among abundant variables from the clinical and molecular profiles of patients. Given a patient's profile, an optimal treatment involves a trade-off between efficacy and toxicity. My research also proposes a novel way to compare treatments with multiple endpoints.