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From: Russell Standish <R.Standish.domain.name.hidden>

Date: Tue, 26 Oct 1999 11:00:47 +1000 (EST)

*>
*

*> On Wed, 20 Oct 1999, Russell Standish wrote:
*

*> > The measure of Jack Mallah is irrelevant to this situation. The
*

*> > probability of Jack Mallah seeing Joe Schmoe with a large age is
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*> > proportional to Joe Schmoe's measure - because - Joe Schmoe is
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*> > independent of Jack Mallah. However, Jack Mallah is clearly not
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*> > independent of Jack Mallah, and predictions of the probability of Jack
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*> > Mallah seeing a Jack Mallah with large age cannot be made with the
*

*> > existing assumptions of ASSA. The claim is that RSSA has the
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*> > additional assumptions required.
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*>
*

*> That's total BS.
*

*> I'll review, although I've said it so many times, how effective
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*> probabilities work in the ASSA. You can take this as a definition of
*

*> ASSA, so you can NOT deny that this is how things would work if the ASSA
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*> is true. The only thing you could try, is to claim that the ASSA is
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*> false.
*

*> The effective probability of an observation with characteristic
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*> 'X' is (measure of observations with 'X') / (total measure).
*

*> The conditional effective probability that an observation has
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*> characteristic Y, given that it has characteristic X, is
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*> p(Y|X) = (measure of observations with X and with Y) / (measure with X).
*

*> OK, these definitions are true in general. Let's apply them to
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*> the situation in question.
*

*> 'X' = being Jack Mallah and seeing an age for Joe Shmoe and for
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*> Jack Mallah, and seeing that Joe also sees both ages and sees that Jack
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*> sees both ages.
*

I shall take X = being Jack Mallah. The rest is irrelevant.

*> Suppose that objectively (e.g. to a 3rd party) Jack and Joe have
*

*> their ages drawn from the same type of distribution. (i.e. they are the
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*> same species).
*

*> Case 1: 'Y1' = the age seen for Joe is large.
*

*> Case 2: 'Y2' = the age seen for Jack is large.
*

*> Clearly P(Y1|X) = P(Y2|X).
*

Sorry, not so clear. It is true by symmetry that p(Y1)=p(Y2).

p(Y1|X) = p(Y1&X)/p(X)

p(Y2|X) = p(Y2&X)/p(X)

Why do you assume p(Y1&X) = p(Y2&X)? I can see no reason. They

certainly aren't symmetrical. About all one can say from symmetry is

p(Y1&X) = p(Y2&Z), where Z = being Joe Schmoe.

Incidently, if you took X to be being anyone (pretty much what you do

by assuming the long clause you gave above) then clearly

p(Y1|X)=p(Y1)=p(Y2)=p(Y2|X). As I said before, though, this has no

relevance to the QTI issue.

*>
*

*> - - - - - - -
*

*> Jacques Mallah (jqm1584.domain.name.hidden)
*

*> Graduate Student / Many Worlder / Devil's Advocate
*

*> "I know what no one else knows" - 'Runaway Train', Soul Asylum
*

*> My URL: http://pages.nyu.edu/~jqm1584/
*

*>
*

*>
*

*>
*

----------------------------------------------------------------------------

Dr. Russell Standish Director

High Performance Computing Support Unit,

University of NSW Phone 9385 6967

Sydney 2052 Fax 9385 6965

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

----------------------------------------------------------------------------

Received on Mon Oct 25 1999 - 18:02:07 PDT

Date: Tue, 26 Oct 1999 11:00:47 +1000 (EST)

I shall take X = being Jack Mallah. The rest is irrelevant.

Sorry, not so clear. It is true by symmetry that p(Y1)=p(Y2).

p(Y1|X) = p(Y1&X)/p(X)

p(Y2|X) = p(Y2&X)/p(X)

Why do you assume p(Y1&X) = p(Y2&X)? I can see no reason. They

certainly aren't symmetrical. About all one can say from symmetry is

p(Y1&X) = p(Y2&Z), where Z = being Joe Schmoe.

Incidently, if you took X to be being anyone (pretty much what you do

by assuming the long clause you gave above) then clearly

p(Y1|X)=p(Y1)=p(Y2)=p(Y2|X). As I said before, though, this has no

relevance to the QTI issue.

----------------------------------------------------------------------------

Dr. Russell Standish Director

High Performance Computing Support Unit,

University of NSW Phone 9385 6967

Sydney 2052 Fax 9385 6965

Australia R.Standish.domain.name.hidden

Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks

----------------------------------------------------------------------------

Received on Mon Oct 25 1999 - 18:02:07 PDT

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