Re: different priors (flat, uniform, etc)
- From: "Reef Fish" <large_nassua_grouper@xxxxxxxxx>
- Date: 27 Oct 2006 06:54:48 -0700
John Uebersax wrote:
Saludos Ruth!
I have a probability on several parameters and one of them is
nuisance one. I want to margizalize over it by simply
integrating the probability along the whole range of values
that such nuisance parameter is allowed to take.
Okay good. You want to "integrate out a nuisance parameter."
Doing it that way is what people call using a flat prior?
I think possibly you're combining two different issues here.
A "prior distribution" is a Bayesian term, and means, basically,
what you think the distribution of a parameter is before
(prior to) some additional data or evidence leads you to
modify your prior beliefs (i.e., produce an updated, or
posterior estimate of the distribution).
That is an EXCELLENT description of what a Bayesian's
prior distribution is. A quantitative description and
summary of a Bayesian's personal opinion/belief of what
he KNOWS about a parameter, to the best of his
knowledge. That is why a TRUE Bayesian is very
SERIOUS about the assessment of his OWN prior, and
not willy-nilly claim ignorance simply because the
description is mathematically intratible or he does not
know how to ellicit his own prior and be able to describe
it in the form of a probability density function.
That is why Robert Schlaiffer had written an entire BOOK
discussing only the computer programs and routines to
help a Bayesian analyze a ONE parameter problem.
So I think we should just dispense with the word "prior"
here. It seems like all you really want to know is: given
that I don't know the shape of my nuisance parameter
distribution, what's a good guess?
That is a completely NON-Bayesian attitude.
Usually one looks to theory for this. Often one just assumes
a normal distribution. That follows when, for example,
the parameter reflects the joint influence of many different factors,
some positive and some negative, such that a bell-shape curve results.
That is not even a good NON-Bayesian approach. You don't
simply ASSUME anything has a normal distribution or any other
disribution. You use data to VALIDATE whether that is even
a reasonable assumption.
I could be wrong, but I believe a "flat distribution" and a "uniform
distribution" would mean the same thing.
You are wrong in your entire understanding of what Bayesian
Statistics is about. A flat distribution as used by pseudo-
Bayesians is NOT necessary a uniform distribution. A uniform
distribution cannot have infinite endpoints, for one thing.
If you could give us some idea of the nuisance parameter, we might be
able
to make suggestions concerning its plausible shape.
Hope this helps.
--
John Uebersax PhD
The OP asks a Bayesian question about uniform priors, flat priors,
uninformative priors, etc. and those are Bayesian concepts.
What you gave is a completely UNEDUCATED answer as well as
a completely inappropriate answer even as a NON-Bayesian.
It is times like this that discussant in sci.stat.math should keep
their mouths SHUT. Your advice to the OP (especially the
bit about "dispense with the word 'prior'" is at best an advice
TO malpractice Bayesian statistics because you don't know
anything about Bayesian statistics yourself.
-- Reef Fish Bob.
.
- References:
- different priors (flat, uniform, etc)
- From: wtplasar@xxxxxxxxx
- Re: different priors (flat, uniform, etc)
- From: John Uebersax
- different priors (flat, uniform, etc)
- Prev by Date: Re: p-value
- Next by Date: Re: different priors (flat, uniform, etc)
- Previous by thread: Re: different priors (flat, uniform, etc)
- Next by thread: Re: different priors (flat, uniform, etc)
- Index(es):
Relevant Pages
|
Loading
