KKARMA <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> 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?
IMO, there are flaws in the Bayesian approach. THe most obvious is
that the sine qua non of the Bayesian approach is the prior
distribution, and this has to be subjectively estimated. In scientific
inference, one wishes to characterize what the *data* say, not what
the researcher thinks. There is more that's wrong with the Bayesian
approach, but in decision applications where subjective preferences
must in any case enter the picture, it is easy to make a virtue of the
Bayesian subjectiveness. Even there, there are problems -- the partial
ordering axiom of subjective probability fails as a behavioral matter.
In addition, and as a matter of principle, the Bayesian approach is
problematic in my opinion in treating uncertainty in particulars
symmetrically with uncertainty in the universals used to model the
occurrence of such particulars. The one is used to talk *about* the
other, therefore putting the two at different levels of semantic
indentation, and precluding any meaningful discourse that would have
instances of the parameter somehow, even in subjectivist metaphor,
varying conjointly with instances of the random variable whose entire
distribution the parameter in some sense models. This is kin to
another objection: the uncertainty from experiment is expressed as a
likelihood function of the model parameters; why should the prior
uncertainty (from the investigator's subjective belief, presumably
deriving from informal experience with the phenomenon in question) be
qualitatively different from likelihood?
The history is also revealing. THe classical methods developed during
the late 19th and early 20th centuries grew out of a *considered
rejection* of the Bayesian device of the probabilistic prior, which
dates back to the 18th century. Starting apparently with Savage in
1954, we have seen a revival of the Bayesian method, with the notion
of subjective probability and associated axiomatization introduced to
provide a less assailable defensive fortress. Subjectivism provides a
mighty fortress indeed, but at the end of the day, some people would
want I think to know what the *data* say. THis might explain the
detente that exists between the classical and (neo-)Bayesian worlds:
the Bayesians seem able to fend off any attack with ever deeper
subjectivism, but they are ill-placed to launch any real attacks of
their own from behind such a fortress.
> Professor of music education
> Sibelius Academy
> Helsinki, Finland
Regards,
S. F. Thomas
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