In article
<63754371-9f33-495d-bb9b-46dafe35f30e@[EMAIL PROTECTED]
>,
aruzinsky <aruzinsky@[EMAIL PROTECTED]
> wrote:
>On Apr 5, 8:27=A0pm, hru...@[EMAIL PROTECTED]
(Herman Rubin) wrote:
>> In article
<ef88f8f9-cb52-4b92-921d-698183138...@[EMAIL PROTECTED]
>com>,
>> aruzinsky =A0<aruzin...@[EMAIL PROTECTED]
> wrote:
>> >On Apr 2, 3:17=3DA0pm, Luna Moon <lunamoonm...@[EMAIL PROTECTED]
> wrote:
>> >> Hi all,
>> >> If my model can be estimated using Maximum Likelihood estimation
>> >> (although the likelihood function is quite complicated where only
>> >> numerical evaluations are possible), are there still benefit of
>> >> turning to Bayesian estimation?
>> >> Thanks!
>> >Is "Bayesian estimation" the same as Maximum a posteriori (MAP)
>> >estimation, which, of course, is better than ML when prior knowledge
>> >is available?
>> No. =A0Bayesian procedures take into account the consequences
>> of the action to be taken.
>> In addition, the maximum can occur at a point with a
>> very sharp peak, while there is a large broad area
>> with a comparable value. =A0Should one choose the peak?
>> I would say not.
>Then it is covered by statistical decision theory?
It was decision theory which led to the current usage
of Bayesian methods. My own philosophy on this, backed
by reasoning on the basis of self-consistency, sometimes
called "coherence", is the prior Bayes risk should be
the criterion. With full choice of procedures and
sufficient computing power, the way to accomplish this
is posterior Bayes, which is what is usually used.
There are many situations in which prior Bayes can be
used, and also this is the way in which robustness
can be evaluated, in which, unfortunately, rash
uses of priors for which easy computation can be
accomplished is substituted for more sound procedures.
The use of conjugate priors, etc., must be justified
on robustness grounds.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@[EMAIL PROTECTED]
Phone: (765)494-6054 FAX: (765)494-0558
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