Poisson models and information theory in ecology, immunology and genomics

Michal Seweryn
Mathematical Biosciences Institute, The Ohio State University

(October 24, 2013 10:20 AM - 11:15 AM)

Poisson models and information theory in ecology, immunology and genomics

Abstract

Poisson abundance models have been widely used in ecology to model species abundance patterns. Also, certain information-based objects (for example Shannon entropy or mutual information) have been adapted to address problems like comparison of diversity or overlap between populations. Application of similar methods to questions related to immunology or genomics is a challenge due to severe under-sampling and sampling errors. 

In the present talk we propose estimators of general measures of entropy based on survey sampling techniques as well as conditional expectations. We analyze consistency and asymptotic normality of such estimators and demonstrate their performance. We also propose a general discrete Poisson mixture modeling framework for T-cell receptor repertoire data and discuss its advantages as well as challenges.