My work is focused on developing and implementing methods for making decisions under uncertainty. I work in stochastic programming, a subfield of mathematical programming that studies optimal decision-making problems when there is uncertainty present in the form of a probability distribution.
My current research studies a method of using observational and/or simulated data to make decisions in the absence of an explicit probability distribution. This is accomplised through use of the statistical likelihood function in the mathematical program. In addition to developing a solution algorithm, I am also exploring how to quantify the value of additional observations for reducing the uncertainty of the problem and finding better solutions.
I am applying this technique to the problem of the use of water in Tucson. In the desert water is especially scarce, and by studying the most economically efficient way to use it I hope to help us conserve water and protect our future.