Applied Math Colloquium

Friday, Nov 9, 2012, 11:30 AM
Cullimore Lecture Hall, Lecture Hall II
New Jersey Institute of Technology


Multiple Decision-Making in the Face of Uncertainty

Edsel A. Pena


Department of Statistics, University of South Carolina



Making decisions is what we all do everyday! And so herein lies the importance of the Science of Statistics since in its very core it is concerned with making decisions, usually in the face of inherent uncertainty in observables and/or in the presence of incomplete information (sample data). In this talk I will first review the solution to the well-known, but fundamental, problem of making a choice between two possible actions (hypotheses). I will then proceed to the problem of multiple decision making where several decisions are to be made simultaneously. The contemporary relevance of such problems arise because of the advent of high-throughput technology, epitomized by the microarray, which enabled the gathering of very high-dimensional and massive data sets. For instance, in the context of microarray data, one is interested in determining the, usually few, genes among thousands and thousands of genes which are actually related to some phenotype of interest. I will describe multiple decision functions that control family-wise error rate and false discovery rate and which improve on existing procedures such as those of the Sidak (controls family wise error rate) and of Benjamini-Hochberg (controls false discovery rate). Interestingly, the solutions to this multiple decision problem can be viewed through an economic lens with errors of decisions serving as the currency of interest.