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


Dr. Michael Newton presented "Gamma-based clustering via ordered means with application to gene expression analysis" on Thursday, March 25, 2010 at 4:30 pm in MATH 175. The talk was co-sponsored by the Department of Statistics Research Colloquium and the Department of Statistics Graduate Student Organization (GSO).


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.


Dr. Newton studies theory, methodology, and application of statistical inference in the biological sciences. Cancer biology has been the source of many recent applied problems, such as linkage analysis to localize genes conferring resistance or susceptibility in rat mammary cancer, and signal identification in cytogenetic or molecular data on cancer genome abnormalities. Problems from microarray expression data are of current interest. Dr. Newton has also contributed to statistical problems in the phylogenetic analysis of molecular sequences. Computational problems have been a focus of his research; he has contributed to the implementation of Markov chain Monte Carlo methods for Bayesian analysis and to the implementation and theory of bootstrap sampling. Further, Dr. Newton has developed new methods of nonparametric Bayesian analysis.

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