In article <9e9tkq$n1$[EMAIL PROTECTED]>,
Robert Dodier <[EMAIL PROTECTED]> wrote:
>I wrote:
>>> Mr. Eckmann is clearly thinking about the probability that
>>> mean1 equals mean2, or the probability that mean1, ..., mean4 are
>>> all equal. There is no reason to dissuade him from this; that the
>>> machinery of classical hypothesis testing is not capable of
>>> handling this suggests that we need to fix the machinery.
>Vadim and Oxana Marmer <[EMAIL PROTECTED]> wrote:
>> I suppose Mr. Eckmann is not intertested in Bayesian approach,
>> so the statement "probability that mean1 equals mean2" has no
>> meaning since mean1, mean2 are not random variables, this
>> probability is either zero or 1.
>Now that's a very interesting assertion -- that probability
>can only be assessed for a random variable.
>Suppose we are asked to bet (or allocate time or other resources)
>on the proposition that mean1=mean2. We are given some data and
>then we must make a decision. How should we bet? How does our
>bet depend on the data? Does it matter whether mean1 and mean2
>are determined from, say, radioactive decay, or if they are
>actually known to a talk show host in another city?
>In many real-life situations, we don't have the luxury of
>refusing to bet -- that is, we can't choose to bet only on
>random variables. We can help find our way out of this mess
>by developing a theory of rational betting on uncertain
>propositions. That theory will have to include assignments
>of degrees of belief to general propositions, not just
>random variables.
This approach to the problem, that of decision making
under uncertainty, can even be done without considering
states of nature to be random. If one assumes that
behavior is self-consistent (this is not over time) then
actions should be compared by "integrating" the evaluation
of the consequences. If one adds some assumptions about
being able to compare consequences with different states
of nature, the resulting integral will be essentially
expectation with respect to a probability measure.
In other words, a "rational" person behaves AS IF there
is a probability distribution on the states of nature.
>Insisting that probability applies only to random variables
>is rather like saying that you can use a ruler to measure
>a train track but not a tree, because a ruler measures length,
>and everybody knows that height is something completely
>different.
>Regards,
>Robert Dodier
--
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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