Re: Programming is the Engineering Discipline of the Science that is Mathematics

From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sun, 11 Jun 2006 19:26:48 GMT
Message-ID: <Y7_ig.20702$A26.476055@ursa-nb00s0.nbnet.nb.ca>

vc wrote:

> Bob Badour wrote:
>

>>vc wrote:
>>
>>
>>>Keith H Duggar wrote:
>>>[Irrelevant stuff skipped]
>>>
>>>Assuming Bayesian treatment (which was not specified originally,  mind
>>>you),  the derivation is still meaningless.  Let's try some argument
>>>from authority:
>>
>>[snip]
>>
>>Your whole dismissal, as I recall, depends on your observation:
>>
>> > P(B|A) def P(A and B)/P(A)

>
>
> It does in the frequentist probability interpretation, yes.
>

>> > the requirement for such definition being that P(A) <>0,  naturally.
>>
>>Keith used the equivalent definition:

>
>
> In the Bayesian interpretation the product rule is a derivation form
> Cox's postulates, but even there P(B|A)P(A) is meaningful only when
> P(A) > 0.:
>

>>From the Jaynes book:

>
> "
> In our formal probability symbols (those with a capital P)
>
>
> P(A|B)
> ....
>
>
> We repeat the warning that a probability symbol is undefined and
> meaningless if the condi-
> tioning statement B happens to have zero probability in the context of
> our problem ...
> "
>
> Please see the book for details.

And since Keith never relied on any meaningful value for P(A|B) in his proof, I wonder what point you are trying to make.

>>P(A and B) = P(B|A)P(A), which places no requirements on P(A) because
>>one does not divide by P(A).

>
> Please see above or the book.
>
>

>>In the case of P(A) = 0, P(A and B) = 0 and P(B|A) is indeterminate,
>>which is to say, we don't care what it's value might be and it could be
>>any real number; although, as a probability, we restrict it to real
>>numbers in the range [0...1].
>>
>>Thus, both of Keith's proofs were entirely valid because he neither
>>inferred nor concluded using the indeterminate P(B|A). He made the valid
>>conclusion that P(A and B) = 0 when P(A) = 0.

Received on Sun Jun 11 2006 - 14:26:48 CDT