[R] p-values

[Frank E Harrell Jr]

On Thu, 29 Apr 2004 14:49:26 +1000
John Maindonald <john.maindonald at anu.edu.au> wrote:

> 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?

I'm sorry to have taken so long in responding to your excellent question
John.  And I'm responding to r-help since the question was posed there
before taking the discussion offline.  

In the words of Don Berry "It takes time to be a Bayesian" and that's the
main reason there are no explicit Bayesian calculations in the book.  I do
make a lot of use of prior information though.  In the future I could see
making some additions to the book along the lines of inclusion of examples
using the MCMCpack package, whose design is appealing to me.

> 
> 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.

Agreed.  I do try to approximate the Bayesian approach with the bootstrap.

> 
> 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?

It's all worth pursuing.  I wish there were already a Bayesian package
that made use of Bayesian methods irresistable.

All the best,

Frank

> 
> 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.
> 
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---
Frank E Harrell Jr   Professor and Chair           School of Medicine
                     Department of Biostatistics   Vanderbilt University