In article <[EMAIL PROTECTED]>, KKARMA <[EMAIL PROTECTED]> wrote:
>As a teacher of research methodology in (music) education I am
>interested in the relation between traditional statistics and the
>bayesian approach. Bayesians claim that their approach is superior
>compared with the traditional, for instance because it does not assume
>normal distributions, is intuitively understandable, works with small
>samples, predicts better in the long run etc.
>If this is so, why is it so rare in educational research? Are there some
>hidden flaws in the approach or are the researchers just ignorant?
>Comments?
Bayesian analysis is not that simple, nor is it claimed
to be. It IS intuitively understandable, but there is
the question of its justification. Any non-Bayesian
procedure can be improved in any real sense by the limit
of Bayesian procedures, which limit need not be quite a
Bayesian procedure. There are no restrictions on sample
size. In this form, it might be very difficult to use.
It is rare in most places, as it disagrees with what are
mistakenly given as the criteria for a statistical procedure.
Testing does not result in fixing a significance level, for
example, although it often corresponds to some standard test
at SOME level. The level varies with sample size, and varies
considerably.
The straightforward Bayes approach is to take a prior
distribution on states of nature. Then one can use Bayes'
Theorem to obtain a posterior distribution. This is a
simple probability result, but is rarely taught in the
standard statistical methods courses, which often avoid
probability.
But this does not justify it. One can get a justification
by assuming self consistent actions; this makes the
quantity to be minimized the expected value of the loss
with respect to some prior measure over the states of
nature, which is Bayesian action. This can often be
approximated even if strict Bayesian computation is too
difficult to carry out.
--
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, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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