##### Speaker

Dr. Jialin Zhang, Mississippi State University

##### Title

Unfolding Entropy

##### Physical Location

Allen Hall 14

**Abstract:** This talk is organized into two parts.

1) Entropy estimation in Turing’s perspective is described. Given an iid sample from a countable alphabet under a probability distribution, Turing’s formula (introduced by Good (1953), hence also known as the Good-Turing formula) is a mind-bending non-parametric estimator of total probability associated with letters of the alphabet that are NOT represented in the sample. Some interesting facts and thoughts about entropy estimators are introduced.

2) Turing’s formula brought about a new characterization of probability distributions on general countable alphabets that provides a new way to do statistics on alphabets, where the usual statistical concepts associated with random variables (on the real line) no longer exist. The new perspective, in turn, inspires some thoughts on the characterization of probability distribution when the underlying sample space is unclear. An application example of authorship attribution is provided at the end.