Wrapping, Mixing, and Estimation for Directional Data - Tomasz J. Kozubowski

Event Date: 

Wednesday, October 28, 2015 -
3:30pm to 5:00pm

Event Date Details: 

Refreshments will be served at 3:15

Event Location: 

  • South Hall 5607F

Event Price: 

Free

  • Department Seminar Series

Directional statistics is an important area, with applications ranging from biology, through earth sciences, to meteorology and medicine. In the first part of the talk, we present a general scheme of generating circular distributions through wrapping linear distributions around a circle, and discuss its particular cases where the linear distribution is either Gaussian or exponential. We then introduce another scheme, where circular distributions are obtained by mixing, and study its relation to wrapping. We show that, in general, these two operations commute: wrapping a mixture of linear distributions corresponds to mixture of wrapped distributions. We explore this in detail, and show that a large number of wrapped circular distributions introduced in the literature can be defined and studied through mixtures of wrapped Gaussian or wrapped exponential distributions. In the second part of the talk, we discuss computational issues arising in estimating circular parameters, where maximum likelihood estimators are rarely available in explicit forms. We present new general methodology, which is based on likelihood and Bayesian principles and can be adapted to circular data.