Peter, I recall that a paper by Art Warrick and Don Myers, back in the
late 80s dealt with this problem. scholar.google.com gave me this as the
reference:
* Optimization of Sampling Locations for Variogram Calculations *
* Warrick, AW; Myers, DE *
* Water Resources Research WRERAQ Vol. 23, No. 3, p 496-500, March 1987.
3 fig, 2 tab, 8 ref. Western Regional Research Project W-155. *
You can also look at the work of Jan Willem van Groenigen, who used
simulated annealing to optimize, among others, your objective.
Best wishes,
--
Edzer
Peter Bossew wrote:
Dear list:
I have the following sampling problem. Given a rectangular regular grid of
c columns and r rows (say 10*10), consisting of c*r cells of equal size. I
want to chose n cells (say 15 out of 100 cells), which can be interpreted
as samples with support equalling the size of one cell, taken from a
regular grid of grid distance = cell size.
According to which pattern do I have to pick the samples (i.e. which cells
do I have to chose) in order to get a frequency distribution of distances
between the centres of the cells (n*(n-1)/2 distances = pairs of cells =
105 in the example) which is as close as possible to uniform, i.e. all
distances occur with about the same probability ?
I tried to solve it numerically, which results in quite strange looking
sampling patterns.
Trying all combinations (r*c over n = 2.53E17 in the example, if I
calculated correctly), is obviously tedious if r,c and n become large. Are
there any analytical solutions ? Any literature about this ?
Thanks for hints,
Peter
-----------------------------------------------------
Peter Bossew
European Commission (EC)
Joint Research Centre (JRC)
Institute for Environment and Sustainability (IES)
TP 441, Via Fermi 1
21020 Ispra (VA)
ITALY
Tel. +39 0332 78 9109
Fax. +39 0332 78 5466
Email: [EMAIL PROTECTED]
WWW: http://rem.jrc.cec.eu.int
"The views expressed are purely those of the writer and may not in any
circumstances be regarded as stating an official position of the European
Commission."
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