Re: name of this problem?

In article <438209dc$1@xxxxxxxxxxxxxx>, David Jones <dajxxx@xxxxxxxxx> wrote:
>stonetiger wrote:
>> I'm sure this sort of problem has been addressed, but I'm having
>> trouble finding anything on it since I don't know what it's called.
>> (I've been calling it a discrimination problem...)

>> Say, for example, you are trying to determine which of 2 options, x
>> and y, is the best (has the highest value of some quanity) . You
>can
>> noisy measurements for each option, but you are allowed only a
>> limited number of measurements and must decide how to use them (i.e.
>> how many times are you will sample x and how many times you will
>> sample y). The objective is to maximize the probability that the
>> option whose measurements have the higher mean is actually the one
>> with the higher value.

<> If you only have 2 options with zero-mean guassian noise on the
<> measurements, then it's not hard to show that you should sample each
<> option in relative proportion to the standard deviation of the noise
<> for the option. However, I'm more interested in the multiple option
<> case and using the only the sample variance instead of the true
>value.

>You could try looking for "two-armed bandit", although this term
>really only applies if outcomes of both choices are each 0-1. You
>could try "sequential decision making". Try "Sequential Methods in
>Statistics" by GB Wetherill, Chapman&Hall, 1966 (possibly later
>editions around).

The term "bandit problems" has been applied to this as
well. Some of Chernoff's papers discuss these. There
are even sequential decisions on which to sample. They
can be surprising, even with only two to decide.

>David Jones




--
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are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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