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Message from discussion Choosing between hypotheses
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Aleks Jakulin  
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 More options Aug 26 2004, 11:20 am
Newsgroups: sci.stat.math
From: "Aleks Jakulin" <a_jakulin@@hotmail.com>
Date: Thu, 26 Aug 2004 17:20:47 +0200
Local: Thurs, Aug 26 2004 11:20 am
Subject: Re: Choosing between hypotheses
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Ross Clement wrote:
> Ray Koopman wrote:

> > The Clopper-Pearson confidence limits for a binomial proportion
> > are the smallest and largest hypothetical values of p
> > that would not be rejected by the observed data.
> > For 9/10 the 95% limits are (.554984, .997471);
> > for 880/1000 they are (.858233, .899499).

> Thanks. This sounds like what I need. As I have data which I can use
> to evaluate the performance of different rule selection strategies,
> can probably apply optimisation techniques to come up the the scalar
> utility function.

You can take advantage of the econometric concept of "value at risk":
pick the model that guarantees better performance, neglecting the
worst X% of situations.

If X=5%, then you would pick the 880/1000 proportion, as the
guaranteed performance is 0.86, while the guaranteed performance for
9/10 is 0.55 (much worse).

This same "value at risk" logic underlies significance testing in
general: prefer the null model except if the alternative will
guarantee you lower error in 95 or 99 or 99.5 percent of samples of
the same size.

--
mag. Aleks Jakulin
http://www.ailab.si/aleks/
Artificial Intelligence Laboratory,
Faculty of Computer and Information Science,
University of Ljubljana,
Slovenia.


 
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