152 Metastatistics for the Non-Bayesian Regression Runner- As it turns out, not even this sentiment is original. From Bickel and Lehmann (2001):
“A chemist, Wilson (1952), [considering some issues in inference] pleads eloquently
that ‘There is a great need for further work on the subject of scientific inference. To
be fruitful it should be carried out by critical original minds who are not only well-
versed in philosophy but also familiar with the way scientists actually work (and not just
with the way some of them say they work).’ Wilson concludes pessimistically: ‘Unfor-
tunately the practical nonexistence of such people almost suggests that the qualities
of mind required by a good philosopher and those needed by a working scientist are
incompatible.’ ” - Of course, a non-Bayesian would feel that^12 is a perfectly good estimator of the variance
if you can’t know which machine produced the measure. - Apparently, many examples of this specific type of inference can be avoided if one is a
“conditional frequentist” (Poirier, 1995, p. 344). - The subtitle of LeCam’s remarks “Toward Stating a Problem in the Doctrine of Chances”
in part was an ironic twist on the title of Bayes’ 1763 classic, “Toward Solving a Problem
in the Doctrine of Chances” (Bayes, 1958). - A term frequently employed instead of “metastatistics” is the philosophy of “induc-
tion,” and there is even debate on whether it is meaningful to talk about inductive
inference. See Neyman (1957) and LeCam (1977), as well as Hacking (2001) and Mayo
(1982). - LeCam’s Basic Principle Zero (LeCam, 1990) was also intended to apply “in particular to
the principles and recommendations listed below and should be kept in mind any time
one encounters a problem worth studying.” LeCam’s principles seem quite sensible to
me, and capture a lot of what I think non-Bayesians have in the back of their minds,
including problems with the use of asymptotic approximations: - Have clear in your mind what it is that you want to estimate.
- Try to ascertain in some way what precision you need (or can get) and what you are
going to do with the estimate when you get it. - Before venturing an estimate, check that the rationale which led you to it is compatible
with the data you have. - If satisfied that everything is in order, try first a crude but reliable procedure to locate
the general area in which your parameters lie. - Having localized yourself by (4), refine the estimate using some of your theoretical
assumptions, being careful all the while not to undo what you did in (4). - Never trust an estimate which is thrown out of whack if you suppress a single
observation. - If you need to use asymptotic arguments, do not forget to let your number of
observations tend to infinity. - J. Bertrand said it this way: “Give me four parameters and I shall describe an elephant;
with five, it will wave its trunk.” - A nice and more complete discussion can be found in Hacking (2001). Much of what
follows is an abbreviated version of Hacking’s discussion. - The Cretaceous/Tertiary Boundary is the boundary between the Cretaceous period and
the Tertiary period. The Cretaceous period is the last period of the Mesozoic Era, which
ended with the sudden extinction of the dinosaursinter alia. - Even here, there is a possible non-Bayesian version of characterizing the probability: if we
could re-run the world 100,000 times, in about 90% of cases an asteroid of size necessary
to lead to mass extinction of the dinosaurs occurs. Perhaps ironically, on this precise
question Bottkeet al.(2007, p. 52) seem to arrive at their conclusion this way: “Using
these [estimated] impact rates as input for a Monte Carlo code, we find there is a≤10%
chance that the K/T impactor was derived from the background and a≥90% chance it
came from the BAF [Baptistina Asteroid family]. Accordingly, we predict that the most