arXiv:1001.3073v1 [stat.ME] 18 Jan 2010 h cetfi ehd hr ewsas influenced also was Pearson’s he Karl by where about method, seriously J. thought scientific and result, the Broad a as D. and, C. Keynes, philoso- Johnson, M. of E. group W. a including by atmosphere, phers influenced this much narrow, In was often regu- activities. Jeffreys own, would college your a in you outside is, discipline, that people still sense meet it the larly as in then, either university was to Cambridge true apparent Cambridge, then. at not them was also of was distinction who the distinct sig- Fisher, though are of of that development those results his from producing in tests, This seen statistics. nificance strikingly operational on most text is importance.” a primarily practical is of It problems the several of treat- of of made methods was ment useful contained mention book the “no the of that that fact reviewers fact criticizes the for he first edition, the second in preface the the use In to to encountered. geophysics, they his data himself, observational for like scientists, then for for famous tools term more provide his Theory, to was the the TP, writing in in aim it sive—main placing by book developments. successfully the recent so of on context which light paper, new splendid sheds this read to I the when Probability appreciated of I him thought Theory I knew there. Faculty also the aca- and joined the 1946–1947, in year Cambridge demic at lectures postgraduate his Lindley Dennis Comment sbs eni h aitra okh rt with wrote he book mathematics magisterial to the wife, attitude in his His seen tool. best a is essential only Theory; an but is the tool, mathematics which produced in atmosphere that the an science, with combined of astronomy, atmosphere philosophy this in is collection It data wrote.) of ever KP thing best the DOI: article Main 183–184 2, DOI: No. 24, Vol. 2009, Science Statistical

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He several posterior, him. with sensible for the a enough over gave good uniform line if attitude real but, Jeffreys’s whole distributions criticize improper his to to and right it Robert are mattered. position; colleagues dominant that rigor, a application mathematical occupy the for was not respect did his high, that while clear is it hserr nasne rssfo iptdphilo- disputed a from arises sense, a in error, This my in where, Theory the in point one is There θ ol ie codn owehryou whether to according differ would 1946 θ a,frJffes ersnainof representation a Jeffreys, for was, .I ih fteeconsiderations, these of light In ). 2 D. LINDLEY only with the accumulation of more evidence that ignorance here—and evaluating the posterior prob- agreement is reached and apparent objectivity ob- ability using what we now call Bayes factors. He tained. Statistical methods, as Haldane pointed out, was not only disagreeing with Neyman and Pearson, are most valuable with modest amounts of data. Jef- but also with Popper, whose philosophy of science freys’s error left the way for de Finetti and Savage to was, and regrettably still is, popular among scien- lay the foundations for Bayesian ideas in a coherent tists. Jeffreys told me that “Popper can’t do proba- way. bility,” and that he had opposed Popper’s election to Let me turn from errors to his triumphs, and the the Royal Society. Bayesians take Jeffreys’s method great concepts that he introduced. One of these is for granted because it can be used effectively in so his Chapter 1 in which he states, and produces a many situations. His work on estimation is less strik- “proof” that uncertainties, always present with mod- ing and he was opposed to the use of a point esti- est amounts of data, must obey the basic rules of mate. The only estimate was the posterior density of probability. It is not, as some eclectic statisticians say today, that one has a choice; one does not, prob- the parameter being considered. His distinction be- ability is the unique tool. Although he never refers tween probability and chance (page 5) is valuable. to them in this context, he was effectively saying Chance is a property of sequences, which de Finetti that Neyman and Pearson were wrong. Confidence later termed exchangeable, so that if you believe a intervals and tail-area significance levels, are not sequence has this property, then you accept chance probability statements about the quantity of inter- and may have beliefs, that is, probabilities, about est and therefore do not satisfy the requirements of its value. The distinction avoids the difficulties when his Chapter 1. Notice that Jeffreys proved that as- probabilities of probabilities are introduced. sertion about probability. The authors of this paper Much modern statistical literature discusses prob- are correct to question the proof, for it does not even lems in a decision framework; for example, referring stand up to the mathematics of 1939, as we in the to a decision to reject a null hypothesis. Yet despite audience saw in 1947, but it makes an important this, there is little statistical literature on practical first step. Actually Ramsey was ahead of Jeffreys, decision problems, using a loss, or utility, function both in time and rigor, and it is astonishing the he representing reality. The Cambridge of the 30s, and did not know of Ramsey’s work, for he lived literally perhaps even later, was concerned with knowledge just down the road. When, in the 1950s, I pointed and learning, feeling that applications were outside this out to him, Jeffreys was also astonished, for he their ivory towers and best left to others. The The- had been at Ramsey’s death bed. What they had es- tablished was that one had to be a Bayesian, there ory reflects this attitude and the occasional refer- was no logical choice. ences to decisions are incidental. In modern terms, In their perceptive analysis, the authors remind he was concerned with the probability of the quan- me that I must have learned from Jeffreys the fact, tity of interest, given the data; and not with deci- to which I now attach much importance, that prob- sions about that quantity, decisions that Ramsey, in- ability is always a function of two arguments. It is fluenced by Keynes, so beautifully discussed. With a defect of much modern instruction in elementary both Ramsey and Keynes, King’s College appears statistics that this is unrecognized and we talk of more practically oriented than Jeffreys’s St. Johns. the probability of an event without mentioning the conditions under which the uncertainty is being con- templated. REFERENCES His second triumph was a general method for the Jeffreys, H. and Swirles, B. (1946). Methods of Math- construction of significance tests, putting a concen- ematical Physics. Cambridge Univ. Press, Cambridge. tration of prior probability on the null value—no MR1744997