11.07.2015 Views

2DkcTXceO

2DkcTXceO

2DkcTXceO

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

D.A.S. Fraser 23922.2 65 years and what’s newI did my undergraduate studies in mathematics in my home town of Toronto,Ontario. An opportunity to study analysis and algebra in the doctoral programat Princeton University arose in 1947. But then, with a side interestin actuarial things, I soon drifted to the Statistics Group led by Sam Wilksand John Tukey. A prominent theme was Neyman–Pearson theory but a persistentseminar interest focussed on Fisher’s writings, particularly those onfiducial inference which had in turn triggered the Neyman (Neyman, 1937)confidence methodology. But also, a paper by Jeffreys (Jeffreys, 1946) keptreemerging in discussions; it offered a default Bayes (Bayes, 1763) approach,often but incorrectly called objective Bayes in present Bayes usage. The strikingthing for me at that time was the presence of two theories for statisticsthat gave contradictory results: if the results were contradictory, then simplelogic on theories says that one or the other, or both, are wrong. This latterview, however, was not part of the professional milieu at the time, thoughthere was some puzzlement and vague acceptance of contradictions, as beingin the nature of things; and this may even be part of current thinking! “Oneor the other, or both, could be wrong?” Physics manages to elicit billions intaxpayer money to assess their theories! Where does statistics stand?With a completed thesis that avoided the frequency-Bayes contradictions,I returned to Canada and accepted a faculty position in the Department ofMathematics at the University of Toronto. The interest in the frequency-Bayes contradictions, however, remained and a conference talk in 1959 andtwo resulting papers (Fraser, 1961a,b) explored a broad class of statisticalmodels for which the two approaches gave equivalent results: the locationmodel f(y − θ), of course, and the locally-generated group extensions, thetransformation-parameter models. Then an opportunity for a senior facultyposition in the Mathematics Department at Princeton arose in 1963, but I wasunable to accept. The concerns for the frequency-Bayes contradictions, however,remained!Now in 2013 with COPSS celebrating its 50th anniversary, we can lookabout and say “What’s new?” And even more we are encouraged to reminisce!There is very active frequency statistics and related data analysis; andthere is very active Bayesian statistics; and they still give contradictory answers.So nothing has changed on the frequency-Bayes disconnect: what goesaround comes around... Does that apply to statistical theory in the 65 yearsIhavebeenintheprofession?Oh,ofcourse,therehavebeenmassiveextensionsto data exploration, to computer implementation, to simulations, and toalgorithmic approaches. Certainly we have Precision, when sought! But whatabout Accuracy? I mean Accuracy beyond Precision? And what about thefrequency-Bayes contradictions in the theory? And even, indeed, the fact thatno one seems to care? And then L’Aquila, Vioxx, Challenger, and of course the

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!