In article
<76da540b-d35c-4915-8292-9e37c32222d4@[EMAIL PROTECTED]
>,
Gary <LanceGary@[EMAIL PROTECTED]
> wrote:
>Herman Rubin wrote:
>> In article
<fe585b87-eaa5-48d9-818f-0a7954c6d99a@[EMAIL PROTECTED]
>,
>> Gary <LanceGary@[EMAIL PROTECTED]
> wrote:
>> >Hypotheses are generated from theories =96 mostly. But competing
>> >theories can sometimes produce the same hypothesis, and they can
>> >differ in how many hypotheses they generate and the precision of the
>> >hypotheses they generate. For example, for a given data set, one
>> >theory might predict one difference between the data points (means,
>> >etc), and another may predict five differences between the data points
>> >(means, etc), perhaps including the difference predicted by the first
>> >theory. One theory might predict that mean X will be higher than mean
>> >Y, while another may predict that X will be higher than Y by precisely
>> >five units. I suppose hypotheses may also differ in how theoretically
>> >significant their predictions are =96 some predictions may be
relatively
>> >trivial and some may be seen as =93im****tant=94, though this kind of
>> >difference in prediction is probably ineluctably subjective.
>> >May query =96 I am not sure it is sensible! =96 is: Is there any
metric or
>> >statistical procedure for examining and investigating these kinds of
>> >differences between theories/hypotheses?
>> >Lance
>> This should be looked at as a statistical decision problem,
>> with priors and losses, or just the product, generated by the
>> user. Attempting to achieve "objectivity" just results in
>> the kind of unanswerable questions you raise.
>> The scientist must provide the metric from his "intuition",
>> and this is of course modified by observations. To see an
>> argument from the point of consistent behavior, see my
>> paper is _Statistics and Decisions_, 1987.
>> --
>Thanks for the reply.
>I haven't read your paper and I don't think I have access to the
>journal either.
>I remembered Bayesian after making the post, though I'm not sure taht
>real scientists think of hypotheses purely in terms of probability. (I
>suspect that your word "intuition" refers to Bayesian concepts of
>belief as probabilities). At any rate I can't see why one can't create
>some kind of metric - this theory makes ten predictions of which 9 are
>true (accord with data), but that theory makes 8 predictions of which
>all 8 accord with data, and the like. Why not?
>Lance
In ALL of my writings on this, since 1947, I have pointed
out that one behaving in a consistent manner acts AS IF
behaving according to a loss-prior combination. It is only
this combination which matters as to choice of proper action.
To illustrate this, suppose we have a finite set Omega of states
of nature, and a finite set A of actions. For any decision
procedure q and any pair (omega,a) there is a probability
P_q(a|omega). What the axioms state is that the choice of
procedure should be based on sum H(omega,a)P_q(a|omega).
Now H(omega,a) can be interpreted as L(omega,a)*pi(omega),
the loss times the prior, to get the usual Bayes formulation,
but I have never claimed it must be.
--
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, Department of Statistics, Purdue University
hrubin@[EMAIL PROTECTED]
Phone: (765)494-6054 FAX: (765)494-0558
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