In article <[EMAIL PROTECTED]>,
Radford Neal <[EMAIL PROTECTED]> wrote:
>In article <yyPs7.55095$[EMAIL PROTECTED]>,
>John Jackson <[EMAIL PROTECTED]> wrote:
>>this is the second time I have seen this word used: "frequentist"? What does
>>it mean?
>It's the philosophy of statistics that holds that probability can
>meaningfully be applied only to repeatable phenomena, and that the
>meaning of a probability is the frequency with which something happens
>in the long run, when the phenomenon is repeated. This rules out
>using probability to describe uncertainty about a parameter value,
>such as the mass of the hydrogen atom, since there's just one true
>value for the parameter, not a sequence of values.
>The frequentist view is currently the dominant one, especially in
>undergraduate statistics courses. The alternative Bayesian philosophy
>holds the contrary view that probability can (and should) be used to
>describe uncertainty even about things that can't conceivably be
>regarded as coming from a sequence of repetitions.
>Confidence intervals are a frequentist concept. Only in the Bayesian
>framework can one say things like, "There's a 95% chance that the
>parameter mu is in the interval (5.4, 7.1)". That, however, is how
>people would like to interpret confidence intervals. You can't
>interpret them that way, though, if you're abiding by the orthodox
>frequentist philosophy.
> Radford Neal
There is another approach, which in my opinion is the only
one which makes sense for "physical" probability, which is
that it exists, and behaves like probability is supposed to
behave. One cannot conduct "independent trials with the
same probability of success"; so the theorem that, if one
could do this, the relative frequencies would converge almost
surely to the true probability is at most a justification, not
a reasonable definition or characterization.
However, this still does not get other than the result that
confidence intervals will contain the parameter with the
specified probability holds BEFORE the analysis of the data.
After the analysis, only the Bayesian approach allows the
type of statement most make.
--
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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