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UW-Milwaukee
Lubar School of Business
Research Seminar Series
Friday October 2, 2015
12:00-1:30 Lubar Hall N440 (Refreshments at 12:00)
Topic:
To Mix or Not to Mix: Trade-offs Between the Options
Speaker: Ehsan S. Soofi
Lubar School of Business
Mixtures of probability distributions appear in various statistical problems at all levels, including comparison of the means of groups, comparison of proportions, regression analysis, choice models, cluster analysis, nonparametric kernel estimation of the distribution function, Bayesian predictive distribution, developing consensus models, measuring uncertainty and disagreement of economic forecasters, and reliability of a system, to name a few. In some problems like regression and clustering one unmixes a mixture in order to gain prediction accuracy for the price of increasing model complexity. In some problems like developing consensus forecasts and kernel estimation one seeks to construct mixtures in order to gain smoothness for the price of increasing uncertainty. Yet, in some other problems like system reliability one has no option and must use both, a mixture (the distribution of lifetime of a system, household income) and its constituents (distributions of the lifetime of components, household members’ incomes). Any reasonable measure provides an assessment of the trade-off between the loss and gain in a mixture problem. The Jensen-Shannon (JS) divergence of mixture has been developed in the information theory and is used in several fields (quantum physics, genomics, bioinformatics, machine learning,and quantitative study of history). However, surprisingly, the JS measure has gone unnoticed in statistics, econometrics, and other quantitative fields. In this talk, I will give examples of the JS for some elementary problems and present results and insights from three of my current projects. In Shoja and Soofi (2015), the JS provides insights for measuring uncertainty and disagreement of economic forecasters about the US inflation rate of the respondents of the Survey of Professional Forecasters of the Federal Reserve Board of Philadelphia. In Beheshti, Racine, and Soofi (2015) the JS provides information measures for nonparametric kernel estimation of the probability distribution function. In a project (with Asadi, Ebrahimi, and Zohrevand) the JS provides information measure for a system in terms of its “signature” defined by the set of probabilities for components to cause a system to fail.
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Mehdi Maadooliat
Assistant Professor, Marquette University
President, Wisconsin Chapter, ASA
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