Linear Estimation of the Probability of Discovering a New Species

Abstract

A population consisting of an unknown number of distinct species is searched by selecting one member at a time. No a priori information is available concerning the probability that an object selected from this population will represent a particular species. Based on the information available after an $n$-stage search it is desired to predict the conditional probability that the next selection will represent a species not represented in the $n$-stage sample. Properties of a class of predictors obtained by extending the search an additional $m$ stages beyond the initial search are exhibited. These predictors have expectation equal to the unconditional probability of discovering a new species at stage $n + 1$, but may be strongly negatively correlated with the conditional probability.