Re: Highest Posterior Density


Reef Fish wrote:
When one chooses the MSE criterion of estimation of sigma^2,
INVARIANCE is out of the window already. In fact, in the
estimation of sigma^2, INVARIANCE is preserved ONLY by
the use of MLE.

Wrong Bob. You need to keep abreast of the literature.

In short, and especially in a Bayesian estimation problem,
there is NEVER any issue of invariance for a true APPLIED
Bayesian, because said Bayesian has to ellicit his own
PRIOR about the chosen parameter theta.

His prior about theta is not going be invariant under any other
nonlinear function of theta -- by definition of CHOICE and
by REASON of probability assessment in the prior distribution.

Wrong again. The prior has nothing to do with it. For example, the
prior

ds f(s)

for some positive real parameter s, is the same measure as

dt g(t)

where g(t) = 2t f(t^{2}) and t is restricted to be positive. Since this
is the same measure, this change does not affect the posterior, which
as I have already explained is independent of the coordinate system.
What is not independent of the coordinate system is the MAP estimate as
it is commonly implemented.

Now are you going to continue to spout nonsense or are you going to
write some equations to prove your point?

illywhacker;

.

Relevant Pages

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