Re: different priors (flat, uniform, etc)


David Winsemius wrote:
"Reef Fish" <large_nassua_grouper@xxxxxxxxx> wrote in
news:1162064508.434519.235090@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:


David Winsemius wrote:
"Reef Fish" <large_nassua_grouper@xxxxxxxxx> wrote in
news:1161965644.243372.111030@xxxxxxxxxxxxxxxxxxxxxxxxxxx:

For Bayesian Inference on the parameter p of a Binomial
distribution or a Bernoulli Process, the beta distribution is a
member of the conjugate prior family -- meaning both the prior AND
posterior belongs to the same distribution family -- Beta.

The uniform distribution on (0,1) is a Beta distribution with
parameters (1,1) and is an INFORMATIVE prior.

Can we hear a bit more about how is Beta(1,1) is an informative prior
for a binomial problem?

It CHANGES the likelihood function to form the posterior distr.

It's in every Freshman textbook in Bayesian statistics.

Some of us will never be Freshman again. How does a uniform prior on
(0,1) change L(.)?

How true. It's too late for you to ask this kind of question about
Bayesian statistics. Go pick up ANY First Course textbook in
Bayesian statistics, and you'll find the answer there.

What you're asking is like someone who walks into this newsgroup
and ask, "what is a sample mean?"

Or perhaps an equivalent question: What would be an uninformative Beta
prior for B(.)?

Didn't remember you said LONG ago that you were glad you don't
have to listen to my free lecture any more?

Perhaps you, Bob O'Hara, and John Uebersax can form a little
study group and learn Bayesian inference about a Binomial p,
like a NON-Bayesian student learn what a Binomial distribution
is.

That's how LOW the LEVEL of you three are in Bayesian statistics.

Go to some other topics in which you know a little SOMETING.

I don't have the patience to teach kintergarden students in any
aspect of statistics.

-- Reef Fish Bob.

.

Relevant Pages

  • Re: different priors (flat, uniform, etc)
    ... distribution or a Bernoulli Process, ... member of the conjugate prior family -- meaning both the prior AND ... posterior belongs to the same distribution family -- Beta. ... The uniform distribution on is a Beta distribution with ...
    (sci.stat.math)
  • Re: What is the conjugate prior for Beta distribution
    ... how can I use some prior information. ... of the distribution while p denotes the "precision" of the ... Thus I need a conjugate prior for Beta distribution. ...
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  • Re: different priors (flat, uniform, etc)
    ... the beta distribution is a member of the ... conjugate prior family -- meaning both the prior AND posterior ... belongs to the same distribution family -- Beta. ... I guess you could mean something similar to the way Fisher treated likelihood: he waved his Fiducial wand, ...
    (sci.stat.math)
  • Re: different priors (flat, uniform, etc)
    ... David Winsemius wrote: ... distribution or a Bernoulli Process, ... member of the conjugate prior family -- meaning both the prior ... The uniform distribution on is a Beta distribution with ...
    (sci.stat.math)
  • Re: different priors (flat, uniform, etc)
    ... as is probably obvious should you look at his history ... John Uebersax PhD ... JU> So I think we should just dispense with the word "prior" ... RF> simply ASSUME anything has a normal distribution or any other ...
    (sci.stat.math)
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