[R] p-values

[John Maindonald]

This is, of course, not strictly about R.  But if there should be
a decision to pursue such matters on this list, then we'd need
another list to which such discussion might be diverted.

I've pulled Frank's "Regression Modeling Stratregies" down
from my shelf and looked to see what he says about
inferential issues.  There is a suggestion, in the introduction,
that modeling provides the groundwork that can be used a
point of departure for a variety of inferential interpretations.
As far as I can see Bayesian interpretations are never
really explicitly discussed, though the word Bayesian does
appear in a couple of places in the text.  Frank, do you now
have ideas on how you would (perhaps, in a future edition,
will) push the discussion in a more overtly Bayesian direction?
What might be the style of a modeling book, aimed at practical
data analysts who of necessity must (mostly, at least) use
off-the-shelf software, that "seriously entertains" the Bayesian
approach?

R provides a lot of help for those who want a frequentist
interpretation, even to including by default the *, **, ***
labeling that some of us deplore.  There is no similar help
for those who want at least the opportunity to place the
output from a modeling exercise in a Bayesian context of
some description.  There is surely a strong argument for
the use of a more neutral form of default output, even to
the excluding of p-values, on the argument that they also
push too strongly in the direction of a frequentist
interpretative framework.

There seems, unfortunately, to be a dearth of good ideas
on how the assist the placing of output from modeling
functions such as R provides in an explicitly Bayesian
framework.  Or is it, at least in part, that I am unaware of
what is out there? That, I guess, is the point of my
question to Frank.  Is it just too technically demanding
to go much beyond trying to get users to understand
that a Bayesian credible interval can, if there is an
informative prior, be very different from a frequentist CI,
that they really do need to pause if there is an
informative prior lurking somewhere in the undergrowth?

John Maindonald.

Frank Harrell wrote:

> They [p-values] are objective only in the sense that
> subjectivity is deferred in a difficult to document way
> when P-values are translated into decisions.


> The statement that frequentist methods are the norm, which I'm
> afraid is usually true, is a sad comment on the state of much
> of "scientific" inquiry.  IMHO P-values are so defective that
> the imperfect Bayesian approach should be seriously entertained.

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Bioinformation Science, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.