Can you give a bit more detail? ]]>

In the regression case, you refer t drawing beta from a prior.

The beta is not drawn fro any prior.

Note that if you do a Bayes analysis with a flat prior you get the

least squares estimator.

Aris Spanos has a different treatment. Dashing, so I may be missing something. ]]>

1. Cox example seems different from the first example by Berger and Wolpert.

In the first example, you see A, so you can condition on it. In the second example, you don’t observe the event you need to condition on. Or did you mean that Fred tells you the result of the coin flip? (in that case it seems obvious, at least to me, that you should condition on the result).

2. In the second case, the ML estimator is known to be ‘only’ asymptotically optimal, but since for d>n is so far from the asymptotic regime, no wonder that another estimator would perform better.

I’m a bit more confused about the bayesian estimator. It seems to me that the issue is not bayesian vs. not bayesian, but whether or not to look at one variable or all. You could put a prior only on beta_1 and get a bayesian estimator which will converge rapidly to the true value.

Also, suppose that the set of beta is indeed generated from the prior which you assume. In this case, will the simple estimator steel beat the bayesian estimator (the latter should be optimal in this case, no?)