A Poisson model for the coverage problem with a genomic application

Suppose a population has infinitely many individuals and is partitioned into unknown N disjoint classes. The sample coverage of a random sample from the population is the total proportion of the classes observed in the sample. This paper uses a nonparametric Poisson mixture model to give new understanding and results for inference on the sample coverage. The Poisson mixture model provides a simplified framework for inferring any general abundance-K coverage, the sum of the proportions of those classes that contribute exactly k individuals in the sample for some k in K, with K being a set of nonnegative integers. A new moment-based derivation of the well-known Turing estimators is presented. As an application, a gene-categorisation problem in genomic research is addressed. Since Turing's approach is a moment-based method, maximum likelihood estimation and minimum distance estimation are indicated as alternatives for the coverage problem. Finally, it will be shown that any Turing estimator is asymptotically fully efficient. Copyright Biometrika Trust 2002, Oxford University Press.