A study of some early investigations into exchangeability. (English) Zbl 0587.01018
The author discusses the notion of exchangeability as it occurs in the work of W. E. Johnson (from 1924), J. Haag (from 1924) and B. de Finetti (from 1928). Johnson’s contribution had been discussed earlier by S. L. Zabell [Ann. Stat. 10, 1091-1099 (1982; Zbl 0512.62007)]. All three earlier authors focussed on a relatively difficult approach via exchangeable events. (The author’s standpoint is to view these contributions in respect of Bayesian statistical inference, infinite exchangeability, and the de Finetti representation theorem.) Rather earlier than any of the authors mentioned, A. A. Chuprov (from 1916 onwards) approached finite exchangeability from the mathematically more elegant standpoint of expectations of ratios of quadratic forms of general exchangeable random variables. For a preliminary report see the reviewer [Chuprov on finite exchangeability, Int. Stat. Inst. 45th Session, contr. Pap., Book 1, 12-22 August, pp. 275-276 (Amsterdam, 1985)].
Reviewer: Eugene Seneta (Sydney)
Keywords:
exchangeability; dependent events; W. E. Johnson; J. Haag; B. de Finetti; statistical inference; de Finetti representation theoremCitations:
Zbl 0512.62007References:
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