a***n
发帖数: 40 | 1 Can a least favorable prior be an improper prior? My impression is that it
can, but it seems not true from the proof of the following theorem.
The theorem is: if Delta0 is a Bayes rule w.r.t. proper prior Pi0, and R(
theta, Delta0) <= r(Pi0, Delta0) for any theta. Then Pi0 is least favorable.
One of the steps of the proof is: integral of "R(delta0, theta)*Pi(theta)"
over theta for any prior Pi, <= sup R(delta0, theta), sup is over theta.
That is, this step takes out sup R(), and it must be true | s******h
发帖数: 539 | 2 Good question. I agree with you that least favorable prior is to compare
priors on 'Proper Priors', i.e. the priors are probability distributions.
It's not we don't want to compare all 'priors including improper ones',
while I think it's very hard for us to compare them, for if we consider all
'priors+improper priors', 'least favorable' may not be that useful or
meaningful.
Consider
parameter space: \Theta={0,1}
In this case the risk set is a convex set on 2-dim space (Euclidean), say S.
For any |
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