# Public Health Dynamics Seminars

## January 14, 2019 - Estimation of Small Tail Probabilities by Repeated Out of Sample Fusion

**Benjamin Kedem, PhD, Professor**

*Department of Mathematics & Institute for Systems ResearchUniversity of Maryland, College Park*

**Monday, January 14, 2019**

12:00 – 1:00 PM

1149 Public Health

*Abstract:*

Often, it is required to estimate the small tail probability p that a quantity such as toxicity level, lead in dust, mercury in fish, chlorophenol in drinking water, methane exposure, plutonium contamination, etc., exceeds an unsafe high threshold. To estimate such a probability, information is needed about large values of the quantity of interest. However, in many cases, the data only contain values below or even far below the designated threshold, which makes the estimation of p challenging. We shall present a novel statistical method whereby, under a mild assumption, it is possible to "peek" into the hidden domain above the threshold, and estimate p by repeated fusion of the given sample with externally generated random data. The consequential estimates based on moderately large samples are surprisingly precise. A comparison with peaks-over-threshold (POT) points to the merit of repeated out of sample fusion. The gist of the method is an iterative procedure for capturing p along a certain curve referred to as a B-Curve. Thus, there is a curve. The curve contains a point "•". We are after that point. The point gives p.

*About the speaker:*

Dr. Benjamin Kedem is a professor, Department of Mathematics & Institute for Systems Research, University of Maryland, College Park. He received a PhD in statistics from Carnegie Mellon University in 1973. His research focuses on spectral and regression methods in time series analysis, time series analysis by filtered zero-crossing counts known as higher order crossings (HOC), semiparametric statistical inference using samples from many sources, and data fusion. HOC has been applied in various time series problems including: discrimination analysis of discontinuous breath sounds, spectral analysis, non-destructive testing and evaluation, earthquake detection, emotion recognition from brain signals, and magnetic anomaly detection. The HOC Theorem of Kedem and Slud appeared in *The Annals of Statistics,* 1982.

Dr. Kedem has authored and co-authored four books and published over 90 papers. He is a Fellow of the American Statistical Association (1999). His research on HOC was selected as an accomplishment by the Air Force Office of Scientific Research (1986), and his 1986 paper "Spectral analysis and discrimination by zero-crossings" was selected as the most outstanding paper reporting original work in any of the Transactions, Journals, and Magazines of the IEEE. He is the recipient of a NASA/GSFC Award (1997), and an IBM Faculty Award (2006). His paper "Bayesian analysis of a density ratio model", published 2017 in the *Canadian Journal of Statistics,* was recognized by the Canadian Statistical Society in June, 2018 "for excellence, creativity, and presentation".