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

It can be useful to know the probabilities that K independent Gamma-distributed random variables attain each of their K! 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 gene expression analysis, which is evaluated, demonstrated, and compared to alternative strategies. The structuring of model components according to inequalities among latent means leads to strict concavity of the mixture log likelihood. The clustering method applies to expression data collected by microarrays or by next-generation sequencing.