🚀 go-pugleaf

In article <BuJ7v8.EKM@mentor.cc.purdue.edu>, hrubin@pop.stat.purdue.edu (Herman Rubin) writes:

> But one thing to keep in mind--the higher the
> dimension, the more important the assumptions.
> -- 

I'm glad to see someone of Prof. Rubin's stature make this statement.  Although
I've spent a good deal of time studying Bayesian methods (I consider myself 
to have mastered the theory up a level represented by Lee's book), I am not
doing mathematical research in this area.  Some very good Bayesians have
made statements similar to Professor Rubin's, namely, that in multi-dimensional
problems the joint behavior of the parameters is more important than their
marginal behavior.  However, I have heard other knowledgeable Bayesians say
that in many problems, the solution is robust to assumptions about joint
behavior.  And I'm willing to admit that I have neither the honed skills nor 
burning interest to investigate the issue for myself.  Intuition tells me Rubin 
is correct.  I would appreciate a brief statement or two from those in the know
about just how serious this problem is.  Is there a wide variety of cases that
are inference robust to assumptions about joint behavior?  Or should I run for
the hills when someone writes, "Assuming *independent* non-informative priors
for theta1 and theta2 . . . "?

(Note:  the use of *non-informative* rather than *improper* or *uniform* was
intentional.  I mean it in the sense of Edwards, Lindman, and Savage where the
priors, while non-informative, are nevertheless, proper.)