Statistics and Data Science Seminar
Prof. Jiping Wang
Northwestern University
A Poisson-compound Gamma model for species richness estimation
Abstract: Suppose D distinct species are observed from an infinite population consisting of N (unknown) distinct species. The estimate of N from popular nonparametric methods can be substantially biased downward, while parametric
approaches assuming a smooth abundance curve in general lack robustness. In this paper we propose a Poisson-compound Gamma approach, where the species
abundance distribution Q is modeled as a Gamma mixture. We first show a nesting property of the Gamma mixture model, under which an arbitrary finite
Gamma mixture can be uniquely re-written as a new Gamma mixture with components sharing a unified shape parameter, and mixed in the mean parameter. Thereby Q can be estimated using nonparametric maximum likelihood
method for any given a. We further propose a least-squares cross-validation procedure for choice of the shape parameter to attain the desired smoothness
of Q while controlling the goodness of fit of the model. The competitive performance of the resulting N-estimator is demonstrated using numerical studies and newly arising genomic data.
Wednesday October 28, 2009 at 3:00 PM in SEO 636