Posted by: jsaaymi April 7, 2008
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I will try to answer this more fully when I have more time.
I think the approach should be:
To simplify and unconfuse and make it boring (which is fun), let it be a distribution of numbers rather than beauties.
Say the numbers are distributed with a probability density function p(x) which is non-zero between MIN and MAX. The judges should choose a threshold based on the number of contestants still remaining to be judged. For the first candidate, let's say we start with a threshold T(1) such that the int_MIN_T(1) p(x) = 0.9 (i.e. the contestant lies in the top 10%).
There is no choice for the last one, so if we have not chosen yet... so T(N) should be MIN
Now, T(n) should be varied in such a way that probability of false detection is minimized. I think this can be solved analytically for simple systems such as uniform distribution.... more detailed analyses are welcome ( i will try this in my leisure )
I think the approach should be:
To simplify and unconfuse and make it boring (which is fun), let it be a distribution of numbers rather than beauties.
Say the numbers are distributed with a probability density function p(x) which is non-zero between MIN and MAX. The judges should choose a threshold based on the number of contestants still remaining to be judged. For the first candidate, let's say we start with a threshold T(1) such that the int_MIN_T(1) p(x) = 0.9 (i.e. the contestant lies in the top 10%).
There is no choice for the last one, so if we have not chosen yet... so T(N) should be MIN
Now, T(n) should be varied in such a way that probability of false detection is minimized. I think this can be solved analytically for simple systems such as uniform distribution.... more detailed analyses are welcome ( i will try this in my leisure )