Re: [Phys-l] estimation competition?

[Brian Blais <bblais@bryant.edu>]

John Mallinckrodt wrote:
> On Apr 29, 2007, at 8:49 AM, Brian Blais wrote:
> > I was thinking it would be fun to have a competition in my class  
> > estimating various
> > quantities.  

> The winning team is the one  
> whose estimate brackets the correct number with the smallest  
> uncertainty. 

That's a nice simple way to get a winner, and focuses on the uncertainty rather than 
the discrepancy, which is also nice.  I wonder how one gets the person who comes in 
second, or third?

How do you compare someone who has a narrow uncertainty window that doesn't bracket 
the correct number (but possible only nearly misses it), with someone who simply has 
a wide uncertainty range, which then has a larger chance of bracketing the correct 
number?

I thought, maybe, looking at the prior odds ratio, assuming the uncertainty is 
Gaussian.  Something like:

compare 1 and 2 =  G(estimate 1, uncertainty 1) / G(estimate 2, uncertainty 2)

where G(e,u) = 1.0/sqrt(2*pi*u**2)*exp(-(e-correct)**2/2*u**2)



			bb


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