In article <8mvea9$78t5j$[EMAIL PROTECTED]>,
Li0N_iN_0iL <LiON iN [EMAIL PROTECTED]> wrote:
>David A. Heiser wrote:
>>von Mises criticizes Fisher (1921) for his introduction of the term
>>"likelihood" without defining it, since in common usage, 'likelihood'
>>and 'probability" have the same meaning.
>Fisher may have addressed this issue in the preface to the thirteenth
>edition of his book, "Statistical Methods", when he wrote:
>"Since the middle of this century a flood of literature has appeared
> bearing on statistical methods. The authors are largely in mathematical
> teaching departments, and better trained as mathematicians than some
> of their predecessors. Too often, however, their experience has not
> included the training and mental discipline of the natural sciences,
> and much space is given to the trivial and the irrelevant."
> -- Sir Ronald A. Fisher (1958)
Fisher could use some mathematics, but he missed the most
important part of mathematics, the use of it as a precise
means of communication and reasoning. You cannot TRAIN a
mathematician; his terminology shows his problems with
understanding what is involved.
Fisher looked upon statistics as a collection of methods,
which already makes understanding a major problem. The
mathematicians attempted to come up with principles upon
which to base methodology, rather than to present methodology
and then attempt to find an argument to justify it.
His "natural science" view was that of objectivity, which the
mathematicians attempted to formalize, and did not succeed as
it was relatively easy to show that, when really pushed, it
was not even possible. He was not a physical scientist; in
the physical sciences, much is developed as a result of the
approach by looking at what is not possible. He could not
appreciate the mathematicians efforts to formalize what he
considered to be "obvious". It may appear to be obvious, but
on careful consideration, the flaws are seen to be of such a
nature that one has to discard a lot of what turns out to be
not only no longer obvious, but even self-contradictory.
>>First of all Fisher is a very ponderous writer, very difficult to find the
>>gold in the pile of ore.
>He seems to have been clear enough with his definition of "likelihood":
>"What has now appeared is that the mathematical concept of probability
> is, in cases in which fiducial probability is not available, inadequate
> to express our mental confidence or diffidence in making such
> inferences, and that the mathematical quantity which usually appears
> to be appropriate for measuring our order of preference among different
> possible populations does not in fact obey the laws of probability. To
> distinguish it from probability, I have used the term "Likelihood" to
> designate this quantity, since both the words "likelihood" and
> "probability" are loosely used in common speech to cover both kinds
> of relationship." -- R.A.F., ibid.
This is totally unclear. I can give a short "definition"
of likelihood; it is probability, or probability density,
considered as a function of the unknown state of nature.
Fiducial probability is an attempt to come up with an
anti-Bayesian approach to posterior probability; as such,
it has the major drawbacks of any such attempt. His
criticism of the limits of Neyman-Pearson was correct;
to remove the limits would require coming up with what
we now know as decision theory.
>>Second, one needs to read Fisher's insight into Bayes original work to
>>understand Fisher's view of probability.
>The only discernable connection between Bayes original work and Fisher's
>view of probability is that they are both discussed in Chapter 2 of his
>1956 book, "Scientific Inference".
--
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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