Re: different priors (flat, uniform, etc)




John Uebersax wrote:
Hi Ruth,

Sorry about Bob (Reef Fish). He's an embarassment to the
newsgroup--and, as is probably obvious should you look at his history
of posts, has the opposite of constructive motives.

What I said in my previous post is correct.

Cheers,
--
John Uebersax PhD

I was very explicit about what John Uebersax said was wrong about
Bayesian statistics:

JU> So I think we should just dispense with the word "prior"
JU> here.

RF> That is a completely NON-Bayesian attitude.

JU> Usually one looks to theory for this. Often one just assumes
JU> a normal distribution. That follows when, for example,
JU> the parameter reflects the joint influence of many different
factors,
JU> some positive and some negative, such that a bell-shape curve
results.

RF> That is not even a good NON-Bayesian approach. You don't
RF> simply ASSUME anything has a normal distribution or any other
RF> disribution. You use data to VALIDATE whether that is even
RF> a reasonable assumption.

RF> I could be wrong, but I believe a "flat distribution" and a
"uniform
RF> > distribution" would mean the same thing.

You WERE wrong! This is one of the most basic ideas in Bayesian
prior distribution that John Uebersax did not even know!!

RF> You are wrong in your entire understanding of what Bayesian
RF> Statistics is about. A flat distribution as used by pseudo-
RF> Bayesians is NOT necessary a uniform distribution. A uniform
RF> distribution cannot have infinite endpoints, for one thing.


JU> What I said in my previous post is correct.

What you said was completely WRONG, and you gave the OP the
worse statistical advice anyone could possibly have given.

Even Anon Bob O'Hara pointed out your error, while he made
his usual error himself which I corrected and provided the OP
the INFO about Bayesian priors relative to the UNIFORM prior:

RF> You are ALMOST correct. That's why I said Uebersax is NOT a
RF> Bayesian. We already know Bob O'Hara isn't one. :-)

RF> The posterior distribution is the likelihood function if the prior
is
RF> "diffuse" (which is NOT the same as a "uniform" or "flat" prior).

which pointed out BOTH John Uebersax and Anon O'Hara were wrong.

Then I proceeded to explain some related concepts and info about
the use the UNIFORM and other prior distributions in that post:

==== begin excerpt
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.

Beta(1/2, 3) is reverse J-shaped.
Beta(1/2, 1/2) is U-shaped, symmetric around 1/2.
Beta(2, 2) is symmetric unimodal, so is Beta(2,3).
Beta(2,1) is the triangular distribution on (0,1)
Beta(3,2) is unimodal, skewed to the left.
Beta(3,1) is J-shaped, so is Beta(2. 1/3).

As you can see, the Beta family CAN represent a wide
variety of opinion about p and hence is a reasonably
good APPROXIMATE prior distribution for one to choose
that best-reflects one's opinion, without having to do any
work on integration of the product of the prior and likelihood,
because the posterior distribution form can be written
IMMEDIATELY given the sample information.

That's the usefulness of a CONJUGATE prior on certain
problems (for Bayesians). However, even the family of
conjugate priors are grossly inadequate for a true Bayesian
for expressing his opinion about a particular p of a
Binomial. That's why Robert Schlaiffer had spent a large
amount of time providing numerical assessment software
and numerical integration software for just that ONE
problem (and other uniariate parameter problems) and
had written a book about it.

==== end excerpt

You, John Uebersax, who hardly EVER had anything correct
or useful to post in sci.stat.math had the GALL to make this
unsubstantiated ad hominem statement about me, in this
particular instance of my correction of your ERRORS and
ill advice? :

Sorry about Bob (Reef Fish). He's an embarassment to the
newsgroup--and, as is probably obvious should you look at his history
of posts, has the opposite of constructive motives.

Look at your OWN (John Uebersax') posting history:

Leaving The Catholic Church Is Not A Solution alt.atheism 3 hours
ago
Leaving The Catholic Church Is Not A Solution alt.atheism 3 hours
ago
different priors (flat, uniform, etc) sci.stat.math 3 hours ago
different priors (flat, uniform, etc) sci.stat.math 23 hours ago
Leaving The Catholic Church Is Not A Solution alt.atheism 23 hours
ago
Orthodoxy, postmodernity and the Emerging Church
soc.culture.south-africa 23 hours ago
Origen and reincarnation (followup) soc.history.ancient 25 hours
ago
The (infamous) regression and correlation discussion -- Summary
sci.stat.edu 3 days ago
{MEDSTATS} Correlation from disturbed data MedStats Oct 14

The current post was the one 3 hours ago. (nothing but ad hominem)
The post 23 hours ago was the one with the ERRORS and bad advice
The (infamous) regression 3 days ago was one of vacuous content

You should stick to your atheism and soc. culture and soc history
newsgroups, and leave out your POLLUTION of statistics groups!

People who live in glass houses shouldn't throw stones, John Uebersax!
JU> look at his history of posts,

This is the MOST RECENT history of MY posts (counted by Google)

511 messages sci.stat.math
61 messages sci.stat.edu
26 messages sci.math
14 messages sci.stat.consult
14 messages alt.sci.math.probability

Principal Component Analysis using R sci.stat.edu 27 minutes ago
My 300th post for the month of October sci.stat.math 7 hours ago
Testing for normality sci.stat.math 9 hours ago
Assessing credibility of a q-q plot by presence of outliers
sci.stat.math 9 hours ago
Principal Component Analysis using R sci.stat.edu 10 hours ago
Experienced Statistician to help decide whether a regression is legitim
sci.stat.math 10 hours ago
Experienced Statistician to help decide whether a regression is legitim
sci.stat.math 11 hours ago
(1 Typo correction) Re: Testing for normality sci.stat.math 15
hours ago
different priors (flat, uniform, etc) sci.stat.math 19 hours ago

Read those for STATISTICAL content and substance.

John Uebersax, you are just ANOTHER one of those who posts in
sci.stat.math who are ignorant in statistics and have nothing but
NOISE to post.

-- Reef Fish Bob.

.