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Topic: "Representative sampling?"
Replies: 10   Last Post: Nov 4, 2000 2:57 PM

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Radford Neal

Posts: 327
Registered: 12/11/04
Re: "Representative sampling?"
Posted: Nov 4, 2000 2:57 PM
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In article <8u1i7r$l7a$1@nnrp1.deja.com>, <robertd@athenesoft.com> wrote:

>However, there is at least one class of interesting problems for which
>deterministic sampling can yield better results than either random
>or stratified-random sampling. This is the class of problems of
>estimating an integral over some space, and for these problems sampling
>sequences can be constructed (so-called "low-discrepency sequences")
>which yield results with less variance than strictly random sampling.

This comparison is a bit of the apples and oranges kind. The variance
for the random sampling is with respect to a random choice of sample
points, with the function being integrated held fixed. The variance
for the deterministic method is for random choice of function, with
the points held fixed. The expected performance of the deterministic
method for your problem will depend on whether the distribution over
functions assumed in deriving this result (a particular sort of
Gaussian process) is close to what your actual prior distribution over
functions is.

Radford M. Neal radford@cs.utoronto.ca
Dept. of Statistics and Dept. of Computer Science radford@utstat.utoronto.ca
University of Toronto http://www.cs.utoronto.ca/~radford

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