112 Metastatistics for the Non-Bayesian Regression Runner
After writing down the problem this way, he then observed that if he were to
draw a number from 12 to 100 he would be indifferent between the outcomes, so
he decided to “focus” on what would happen if he should draw between 1 and
- By doing so, he decided that, in the case of a subsidiary problem – ignoring
outcomes higher than 11 – the correct answer depended on whether he would “sell
an outright gift of $500,000 for a 10 to 1 chance to win $2,500,000 – a conclusion
that I think has a claim to universality, or objectivity.” He then concluded that,
while it was still true thatCD, upon reflectionAB, not the other way around.
As Savage himself noted: “There is, of course, an important sense in which pref-
erences, being entirely subjective, cannot be in error; but in a different, more subtle
sense they can be.”
We put aside the frequently knotty subject of “prior beliefs” for the moment, and
contrast this Bayesian view with a typical non-Bayesian view about “what statistics
is good for.”
3.3.2 What is statistics good for? A non-Bayesian view
In its most restricted form [statistical] theory seems to be well adapted to the
following type of problem. If two persons disagree about the validity, correctness
or adequacy of certain statements about nature they may still be able to agree
about conducting an experiment “to find out”. For this purpose they will have
to debate which experiment should be carried out and which rule should be
applied to settle the debate. If one of them modifies his requirements after the
experiment, if the experiment cannot be carried out, or if another experiment is
used instead, or if something occurs that nobody had anticipated, the original
contract becomes void. Since the classical theory is essentially mathematical
and clearly not normative it is rather unconcerned about how one interprets
the probability measures...The easiest interpretation is probably that certain
experiments such as tossing a coin, drawing a ball out of a bag, spinning a
roulette wheel, etc., have in common a number of features which are fairly
reasonably described by probability measures. To elaborate a theory or a model
of a physical phenomenon in the form of probability measures is then simply
to argue by analogy with the properties of the standard “random” experiments.
The classical statistician will argue about whether a certain mechanism of
tossing coins or dice is in fact adequately representable by an “experiment” in
the technical stochastic sense and he will do that in much the same manner and
with the same misgivings as a physicist asking whether a particular mechanical
system is in fact isolated or not. (LeCam, 1977, p. 142)A non-Bayesian doesn’t view probability as a singular mechanism for deciding
the probability that a proposition is true. Rather, it is a system that is helpful for
studying “experimental” situations where it might be reasonable to assume that
the experiment is well described by some chance set-up. Even when attempting to
use “non-experimental” data, a non-Bayesian feels more comfortable when he/she
has reason to believe that the non-experimental situation “resembles” a chance set-
up. Indeed, from a strict Bayesian viewpoint it is hard to understand why, in the