In what sense is statistical inference inference?

Probably the most general formulation of the behavioristic approach,
which derives Bayesian-type procedures as a conclusion from
rationality, is my paper in _Statistics and Decisions_, 1987.  This
paper also indicates why, given certain assumptions about consistency
of behavior, consistent group action must essentially be dictatorial.

There is an extensive literature.  Much of it is intended for people in
economics and management; Raiffa's _Decision Analysis_ is an easily
understood book on the problems of utility, and points out the
difficulties there.  This even occurs without the inference problem.
A higher-level book, on the level of the typical beginning mathematical
statistics text, and written as a textbook, which discusses the
inference problem is that by J. O. Berger, _Statistical Decision
Theory_.

But, other than a hope for the existence of "scientific objectivity",
should two people be expected to take the same action?  Careful
consideration of the problems of inference shows that the data can
only change the acceptance of the individual theories, and not produce
the theories.  Indeed, as was possibly first pointed out by me, the
problem in hypothesis testing is when to "accept" a theory known to be
false, and which possibly does not even "fit" the data.  This is
becoming increasingly important, as accurate data is becoming easier,
and accurate theories are becoming harder.

-- Herman Rubin <hrubin@pop.stat.purdue.edu>

[ Editor: from a reply mailed to Chris Cole, August 1991, under the
subject line used as the problem here. ]