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Charles Darwin

Exercise 9.1.

When Charles Darwin first landed on the Galapagos Islands in September 1835, he had no idea how many different species of plants he would find there. Having examined n = 122 specimens, and finding that they can be classified into m = 19 different species, what is the probability that there are still more species, as yet unobserved? At what point does one decide to stop collecting specimens because it is unlikely that anything more will be learned?

This problem is much like that of the sequential test of Chapter 4, although we are now asking a different question. It requires judgment about the real world in setting up the mathematical model (that is, in the prior information used in choosing the appropriate hypothesis space), but persons with reasonably good judgment will be led to substantially the same conclusions.

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