Some Thoughts About the Relations Between Statistics and Probability Theory

• Activity Number: 273
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 8:00 PM to 9:30 PM
• Sponsor: IMS
• Author(s): Erwin Bolthausen*
• Companies: University of Zurich

Abstract

Traditionally, there had been very close relations between statistics and probability theory. This is already present in the work of Bernoulli, whose motivations to prove the strong law of large numbers had been his thoughts about the consistency of statistical estimators. Also much later, many important developments in probability theory had been triggered by questions in statistics, like the asymptotic distribution of the Kolmogorov-Smirnov statistic, or large deviation theory which has partly been motivated by efficiency considerations in statistics. In the past decades, probability theory saw many important developments which have seemingly no relations with statistics, like Schramm Loewner equations, spin glasses, random media, and many others. As a consequence, there is no longer an equally intensive communication between the two communities, as it had existed before. Based on a number of examples, I will try to argue that this is for both sides not an ideal situation. Being a probabilist, and talking at a statistics meeting, the viewpoint will of course be biased.