|Dr. Donald Richards, Department of Statistics, Penn State University|
|Title:Distance Correlation: A New Tool for Detecting Association and Measuring
Correlation Between Data Sets
Abstract: The difficulties of detecting association, measuring correlation, and establishing cause and effect have fascinated mankind since time immemorial. Democritus, the Greek philosopher, underscored well the importance and the difficulty of proving causality when he wrote, “I would rather discover one cause than gain the kingdom of Persia.’’
To address the difficulties of relating cause and effect, statisticians have developed many inferential techniques. Perhaps the most well-known method stems from Karl Pearson’s coefficient of correlation, introduced in the late 19th century.
I will introduce in this lecture the recently-devised distance correlation coefficient and describe its advantages over the Pearson and other classical measures of correlation. We will review an application of the distance correlation coefficient to data drawn from large astrophysical databases, where it is desired to classify galaxies according to various types. Further, the lecture will analyze data arising in the on-going national discussion of the relationship between state-by-state homicide rates and the stringency of state laws governing firearm ownership.
The lecture will also describe a remarkable singular integral which lies at the core of the theory of the distance correlation coefficient. We will describe generalizations of this singular integral to truncated Maclaurin expansions of the cosine function and to the theory of spherical functions on symmetric cones.