The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.stat.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Radford Neal

Posts: 327
Registered: 12/11/04
Re: "Representative sampling?"
Posted: Nov 4, 2000 2:57 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <8u1i7r$l7a$>, <> 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
Dept. of Statistics and Dept. of Computer Science
University of Toronto

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.