[BLML] BLML exchange
Brian
bmeadows666 at gmail.com
Fri Aug 30 01:08:07 CEST 2013
Fair enough, Jerry, I take your word for it. It was an honest question
- my maths background finishes at standard deviations and confidence
limits. I didn't know whether or not a 'real world' observational
uncertainty would change anything. I certainly wasn't questioning your
competence in any way.
My bias against figures which imply greater-than-practical accuracies
is no doubt due to a strict regime of 'no error estimations = halve
the marks' from my undergraduate days.
On 08/29/2013 10:27 AM, Jerry Fusselman wrote:
> On Thu, Aug 29, 2013 at 7:18 AM, Brian <bmeadows666 at gmail.com> wrote:
>> On 08/29/2013 07:36 AM, Alain Gottcheiner wrote:
>>
>> <snip>
>>
>>> That's what I like with my fellow mathematicians. They call such a proof
>>> 'easy'.
>>> But it is correct.
>>>
>>
>> Mathematically correct, maybe - but having been educated as a chemist
>> rather than a mathematician, reading something which implies that a
>> bridge player can time the accuracy of partner's bid at the table to
>> +/- 0.05 of a second makes me automatically sceptical about what's
>> being said.
>
> It would have been incompetent of me to supply a proof that works only
> because I used continuous random variables. The proof generalizes to
> discrete random variables, but using discrete random variables would
> not have been fair to Steve. He postulated the existence of a point
> that provides no UI, and using continuous random variables is the only
> way he could possibly be right. (Actually, he is right if he limits
> himself to *two* possible meanings of the bids and he requires the
> densities to have overlapping convex supports and to be continuous
> with continuous contact with zero---but these assumptions strike me as
> unrealistic.)
>
>>
>> If Jerry had said "Assume that your partner makes his bid in 4 seconds
>> +/- 1 second" then that would seem far more realistic to me. I'm not
>> enough of a mathematician to know whether the proof holds up when you
>> introduce real-world observational uncertainties.
>>
>
> Yes, the proof still holds up if I had said "Assume that your partner
> makes his bid in 4 seconds
> +/- 1 second" and the numbers are exactly the same, because
>
> p(N|s=4+/-1) = p(s=4+/-1|N)p(N) / (p(s=4+/-1|N)p(N) + p(s=4+/-1|A)p(A)),
>
> and all the same numbers work---p(s=4+/-1|N) = 1 still, and
> p(s=4+/-1|A) = 1/6 still. The end result of seeing that the bid takes
> 4 seconds +/- 1 second is still to change your thinking from p(N) =
> 20% to p(N|s=4+/-1) = 60%. It's still UI.
>
> Jerry Fusselman
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