Estimation of Tail Probabilities by Repeated Augmented Reality

Benjamin Kedem; Saumyadipta Pyne

doi:10.1007/s42519-020-00152-1

Estimation of Tail Probabilities by Repeated Augmented Reality

J Stat Theory Pract. 2021;15(2):25. doi: 10.1007/s42519-020-00152-1. Epub 2021 Jan 20.

Authors

Benjamin Kedem¹, Saumyadipta Pyne^{2

3}

Affiliations

¹ Department of Mathematics, Institute for Systems Research, University of Maryland, College Park, MD USA.
² Public Health Dynamics Laboratory, Department of Biostatistics, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA USA.
³ Health Analytics Network, Pittsburgh, PA USA.

Abstract

Synthetic data, when properly used, can enhance patterns in real data and thus provide insights into different problems. Here, the estimation of tail probabilities of rare events from a moderately large number of observations is considered. The problem is approached by a large number of augmentations or fusions of the real data with computer-generated synthetic samples. The tail probability of interest is approximated by subsequences created by a novel iterative process. The estimates are found to be quite precise.

Keywords: B-curve; Density ratio model; Iterative process; Repeated out of sample fusion; Residential radon; Upper bounds.