Good, Jekinek, Mercer, and Robbins on Turing's Estimate of Probabilities

SYNOPTIC ABSTRACT

A.M. Turing, in a 1941 personal communication to I.J. Good, suggested a formula for estimating probabilities of words in text and, more generally, of species in a mixed population of various species. The formula is particularly interesting in a “small sample” situation where events of interest did not occur at all. It is remarkable that Turing's formula can be obtained by significantly different statistical methods.

Key Words and Phrases:

• estimation
• small probabilities
• sparse data
• unobserved events
• unseen species
• language models