Mathematics Colloquium: Ben Kedem, "Augmented Reality in the Estimation of Small Tail Probabilities"

Wednesday, September 5, 2018
3:15 p.m.
3206 Kirwan Hall

Mathematics Colloquium

Augmented Reality in the Estimation of Small Tail Probabilities

Professor Benjamin Kedem
Department of Mathematics
Affiliate Faculty, Institute for Systems Research
University of Maryland

Abstract
Often, it is required to estimate the probability that a quantity such as mercury, lead, toxicity level, plutonium, temperature, rainfall, damage, wind speed, risk, pollution, flood, etc., exceeds an unsafe high threshold. The probability in question is then very small. To estimate such a probability, information is needed about large values of the quantity of interest. However, in many cases, the data are far from being “BIG” and only contain values far below the designated threshold, let alone exceedingly large values, which ostensibly renders the problem insolvable. It is shown that by repeated fusion of the data with externally generated random data we can create a curve containing a point which essentially coincides with the tail probability of interest. An iterative method for “capturing” the point will be described and illustrated. The method provides relatively short, yet reliable, interval estimates based on moderately large samples. From the Internet: “In the past twenty years a vast new body of extreme value theory was developed, referred to as ‘peaks over threshold modeling.’ This theory allows the use in the analysis of all data exceeding a sufficiently high threshold, a feature that may result in improved extreme value estimates.” A comparison of the repeated fusion approach with peaks over threshold (POT) across different tail types, using both artificial and real data, will be presented.

Audience: Graduate  Undergraduate  Faculty  Post-Docs 

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