Re: [sdpd] Re: Another 2 pence worth

["ROBIN SHIRLEY (USER)" <R.Shirley...@surrey.ac.uk>]

Armel wrote:

> There are comments about the Bayes's theorem in the Encyclopedia of
> Physics (VCH, 2nd Edition, 1991, p.962) that seems to put some
> doubt about it. I cite just a part of the comments :

> "The difficulty of the theorem lies in interpreting what is meant
> by the prior and posterior "probabilities" of a hypothesis, though
> if these can be somehow surmised, the theorem tells us (or should
> tell us) how experiment ought to influence our attitude to a
> hypothesis. Presumably (though this presumption has been a
> battleground among scientists and philosophers for over 200 years)
> we should prefer the hypothesis with the greatest posterior
> probability". etc.  

I've taught statistics for a number of years, and also introduce my
students to Bayesian methods.  One needs to use caution when
interpreting the mainstream statistics literature of a decade or two
back, like (perhaps) the encyclopedia article that you quote,
because for many years the conventional wisdom had been to assume
(wrongly) that there was something invalid about Bayes equation.

It is now recognised that this is not the case.  On the other hand,
Bayesian methods have suffered from the excessive enthusiasm of some
latter-day Bayesians, who have claimed (also wrongly) that it is a 
quite new approach which presents an alternative to traditional 
(distribution-based) statistics.

In fact distributionist inferential statistics must also introduce 
subjective probability in order to be logically complete, and there 
is no conflict between Bayesian and distributionist approaches, if 
both are used correctly (as of course must be the case, unless 
one or both are invalid).

Thus, where the relevant distributions are available, the best way
to obtain Bayesian prior probabilities is indeed through standard
distribution-based approaches.  Where they are not, however, we have
to make up the priors (which is what subjective probability is all
about). However they will then not be as good estimates as if they
had been based on the appropriate distributions.

Best wishes

Robin Shirley

---------------------------------------------------------

To:            sdpd...@egroups.com
From:          "Armel Le Bail" <alb...@cristal.org>
Date:          Wed, 25 Oct 2000 07:36:16 -0000
Reply-to:      sdpd...@egroups.com
Subject:       [sdpd] Re: Another 2 pence worth

Kenneth wrote :

> As regards the space group determination problem,
> I can recommend watching out for the Jan 2001 issue
> of Acta A, which will contain a paper from RAL by
> Anders Markvardsen on that very topic.  It outlines
> a probabalistic approach to SG detn from powder data
> that puts SG detn on a fully quantitative basis.

Bayesian salt I suppose ?

We have seen in the last 10 years the Bayes's theorem
applied to almost all topics in crystallography. And
in all cases, well, this is always better with Bayes
than without Bayes...

There are comments about the Bayes's theorem in the
Encyclopedia of Physics (VCH, 2nd Edition, 1991, p.962)
that seems to put some doubt about it. I cite just
a part of the comments :
"The difficulty of the theorem lies in interpreting what
is meant by the prior and posterior "probabilities"
of a hypothesis, though if these can be somehow
surmised, the theorem tells us (or should tell us)
how experiment ought to influence our attitude to
a hypothesis. Presumably (though this presumption
has been a battleground among scientists and
philosophers for over 200 years) we should prefer
the hypothesis with the greatest posterior probability".
etc.  

My approach of SG determination is more pragmatic
than probabilistic : if the space group is ambiguous
then I test all apparently possible space groups.
Ambiguity may come naturally (space groups with same
extinctions) or due to overlapping. Not that complex.
I would not give the decision to any probabilistic
software. I prefer to decide myself.

Best,

Armel Le Bail
http://www.cristal.org/course/








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