Statistics Seminars, Spring 2012

• Organizer: Abram Kagan
• Link to seminar schedules from previous years
• Link to the program for Advances in Statistics and Applied Probability: Unified Approaches, A Symposium in Honor of Benjamin N. Kedem, July 30-31, 2009
• Statistics Consortium Seminars and Workshops

Spring 2012 Talks

SPEAKER: Dr. Yaakov Malinovsky, Dept. of Math. and Stat., UMBC
University of Maryland
Baltimore, MD USA

TITLE: Monotonicity in the Sample Size of the Length of Classical Confidence Intervals Abstract

TIME AND PLACE:  February 9, 2012, 3:30pm
              Room 1313, Math Bldg.

ABSTRACT: It is proved that the average length of standard confidence intervals for parameters of gamma and normal distributions monotonically decreases with the sample size. Though the monotonicity seems a very natural property, the proofs are based on fine properties of the classical gamma function and are of independent interest. (It is a joint work with Abram Kagan).

SPEAKER: Prof. Davis Hamilton, Dept. of Mathematics, Univ. of Maryland
University of Maryland
College Park, MD USA

TITLE: An Accurate Genetic Clock and the Third Moment

TIME AND PLACE:  February 16, 2012, 3:30pm
              Room 1313, Math Bldg.

ABSTRACT: The genetic clock uses mutations at molecular markers to estimate the time T1 of origin of a population. It has become important in the evolution of species and diseases, forensics, history and geneology. However the two types of methods used yield very different estimates even from the same data. For humans at about 10,000 ybp .Mean square Estimates. (MSE) give results about 100% more than .Bayesian analysis of random trees. (BAT). Also the SD are about 50% of T1. (In the last 500 years all methods give similar and accurate results). Our new theory explains why MSE overestimates by about 50%, while BAT underestimates by about 25%. This is just not a mathematical problem but involves two quite different physical phenomena. The first comes from the mutation process itself. The second is macroscopic and arises from the reproductive dominance of elite lineages. Our method deals with both giving 15% accuracy at 10,000 ybp. This is precise enough to resolve a question first mentioned in Genesis, argued over by archeologists and linguists(and Nazis): the origin of the Europeans. The theory depends on solving a stochastic system of infinite dimensional ode by hyperbolic Bessel functions. At the heart is a new inequality for probability distributions P normalized with mean . = 0, variance _ = 1: If the third moment ! > 0 we have P(1,+1) > 0.