262 Statistical discussion forum

restrictive than our (2). Moreover, the convergence holds in all x e (0, 1) p a t which g is continuous.

This research was supported by the Alexander von Humboldt Foundation.

References

Ahmad, I.A. and P.E. Lin (1984). Fitting a multiple regression function. J. Statist. Plann. Inference 9, 163-176.

Georgiev, A.A. (1985). Proprirt~s asymptotiques d'un estimateur fonctionnel non paramrtrique. C.R. Acad. Sci. Paris. Ser. I 300, 407-410.

Georgiev, A.A. and W. Greblicki (1986). Nonparametric function recovering from noisy observations. J. Statist. Plann. Inference 13, 1-14.

Priestley, M.B. and M.T. Chao (1972). Non-parametric function fitting. J. Roy. Statist. Soc. Ser. B 34, 385-392.

Alexander A. Georgiev Ruhr-Universit~it Bochum Lehrstuhl fiir Elektrische Steuerung und Regelung Postfach 102148, D-4630 Bochum 1, West Germany and Technical University o f Wroclaw Institute o f Engineering Cybernetics Wyspianskiego 27, PL-50370, Poland

F6. Graig the Vague

Stigler (1986) takes some quarter-baked ideas of Craig (1699) and largely bakes them. As I have often dabbled with partly-baked ideas, I have sympathy with Stigler's article but I have the following criticisms and comments.

(i) P r (E [H) is not a likelihood, in the sense in which the term was introduced in 1925 by Fisher and in the sense in which is it usually used, unless H is a simple statistical hypothesis, but it has been called a Bayesian likelihood (Good, 1978, 1982). A likelihood, as usually understood, is a non-Bayesian concept. When E denotes the reasonably relevant historical evidence, and H denotes say the resurrec- tion of Christ, the probability Pr(E [H) has almost no meaning to a non-Bayesian.

(ii) Stigler's expression (2), which he misleadingly calls a log-likelihood ratio (it looks like one) is often and better called a weight of evidence, at least by me in countless publications. Stigler's knowledge of the history of statistics up to 1900 is outstanding but here he distorts more modern history. For the relevant history, which goes back at least to 1878, see Good (1983/85) where C.S. Peirce, Dorothy Wrinch & Harold Jeffreys, and A.M. Turing are cited.

(iii) Stigler says that "our past can be taken from us by a series of unreliable historians". True and important, and historians cannot get very close to reliability (even when, unknown to us, they get close to the truth) because historians are forced

Statistical discussion forum 263

to rely mainly on published work, whereas the past involved conversations and un- published manuscripts that can never be retrieved. Our past has been largely taken from us willy-nilly by the ravages of time and indeed that is one of Craig's themes according to Stigler. Compare, for example, West (1985).

(iv) One can infuse modern meaning into the ancient Greek concept of Themis, the Goddess of Justice, with her two scales, and this was done in Good 0983/85). So we can go back long before 1699 when looking for partial anticipations of the technical concept of weight of evidence. It captures the main linguistic sense; see Good (1984).

References

Good, I.J. (1978). Are maximum-likelihood estimates invariant? C10 in J. Statist. Comput. Simulation

7(1), 80-81. Good, l.J. (1982). Bayesian likelihood, a point of terminology. C130 in J. Statist. Comput. Simulation

15(1), 84-85. Good, I.J. (1983/85). Weight of evidence: a brief survey. In: J.M. Bernardo, M.H. DeGroot, D.V.

Lindley, and A.F.M. Smith, Eds., Bayesian Statistics 2: Proceedings of the Second Valencia Interna- tional Meeting 6/10, 1983. North-Holland, New York, 249-269 (including discussion).

Good, l.J. (1984). The best explicatum for weight of evidence. C197 in J. Statist. Comput. Simulation 19(4), 294-299.

Stigler, S.M. (1986). John Craig and the probability of history: from the death of Christ to the birth of Laplace. J. Amer. Statist. Assoc. 8i, 879-887.

West, Nigel (1985). A Threat of Deceit: Espionage Myths of World War II. Dell, New York.

I.J. Good

F7. Some improvements in statistical and other 'literature'

For Read

(i) iff

(ii)

*(iii)

*(iv)

(v)

(vi)

(vii)

most everywhere

most all x

denoted x

The matrix was inverted Penrose

Robinson Crusoe said "I ' l l see you Friday, Friday"

shop Krogers

ifif (because this is unambiguously prounceable and could be regarded as a word)

almost everywhere

almost all x

denoted by x (the preposition is essential)

The matrix was inverted by Penrose [or] The matrix was inverted, Penrose

Robinson Crusoe said 'TII see you on Friday, Friday".

shop at Krogers [It isn't essential to omit prepositions!]