Yesterday I learned something interesting from a talk given by Professor Bikas K Sinha. The following is an excerpt from the reference [1], which exactly shows the interesting point of the problem.

“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.”

Searcher: “I am contemplating extending my initial search an additional m stages, and will so do if the expected number of individuals I will select in the second search who are new species is large. What do you recommend?”

Statistician: “Make one more search and then I will tell you.”

Refer to the Annals of Statistics paper:

[1] Starr, Norman. “Linear estimation of the probability of discovering a new species.” The Annals of Statistics (1979): 644-652.

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