The Finding that Shocked the World: Stein's Paradox by Demian Gass '20

The Finding that Shocked the World: Stein’s Paradox by Demian Gass ’20, Statistics Colloquium, Wednesday, March 4, 1:10 – 1:50 pm, Stetson Court Classroom 105

Abstract:  Sometimes a mathematical result is strikingly contrary to a generally held belief even though an obviously valid proof is given. Charles Stein of Stanford University discovered such a paradox in statistics in 1955.  Stein’s paradox concerns the use of observed averages to estimate unobservable quantities.  In traditional statistical theory, it can be proven that no other estimation rule is uniformly better than the observed average; however, the paradoxical element in Stein’s result is that it sometimes contradicts this fundamental law of statistical theory.  The statistician who employs Stein’s method can expect to predict the future averages more accurately than if they simply used the observed averages.  More specifically, if we have three or more observed independent variables, of which we would like to find a good estimator for their future means, then there is a procedure that is better than simply extrapolating from the three separate averages of the observed values. Stein’s method is widely applicable, finding usage in functions such as predicting MLB batting averages, identifying incidence of Toxoplasmosis in Central America, and a broad spectrum of other topics.  In my colloquium talk, I will be presenting and proving Stein’s Paradox, discussing some of its many applications, and explaining its important relation to empirical Bayesian statistics.