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Re: "Representative sampling?"
Posted:
Nov 4, 2000 2:57 PM


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 stratifiedrandom sampling. This is the class of problems of >estimating an integral over some space, and for these problems sampling >sequences can be constructed (socalled "lowdiscrepency 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 



