GSO Spring Speaker 2010

Gamma-based clustering via ordered means with application to gene expression analysis

Michael Newton
Professor
Departments of Statistics and of Biostatistics & Medical Informatics, University of Wisconsin-Madison

Venue: MATH 175

Abstract:

It can be useful to know the probabilities that N independent Gamma-distributed random variables attain each of their N! possible orderings. Each ordering event is equivalent to an event regarding independent negative-binomial random variables, and this finding guides a dynamic-programming computation. Gamma-rank probabilities are central to a model-based clustering method for multi-group expression analysis, which I will discuss, demonstrate, and compare to alternative strategies. The structuring of model components according to inequalities among latent means leads to strict concavity of the mixture log likelihood, which is convenient computationally. The clustering method applies to expression data collected by microarrays or by next-generation sequencing. I will also discuss other applications of the gamma-rank probabilities.