Re: The intensity of a 2 dimensional poisson pattern from limited observational data


<Bouldin@xxxxxxxxxxx> wrote in message
news:1187742199.418061.18150@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Here's a problem I'm trying to solve. Given an observed two
dimensional poisson process (e.g. tree spatial locations in a forest),
I would like to infer the intensity of the process (tree density in
the forest in this case, = trees per unit area) based on certain
empirical observations. Those observations are a set of locations of
pairs of trees relative to randomly chosen points, with the random
points being far apart relative to the proximity of the two trees to
each point. That is, I know the x and y coordinates of 2 trees and a
nearby random point for a large number of well-spaced random points
throughout a large area. Therefore at each random point I know the
distance from the point to tree 1, from the point to tree 2, and the
distance between the two trees.
[...]

I don't think you have enough information to do what you want. (Or if you
do, you haven't said so in your first two posts.) You need some sort of
model for how the pairs of trees were chosen.

For example, for all you've said, the two trees might be the nearest two oak
trees to the "randomly" or "+/- regularly distributed" points. Apart from a
lower bound on the overall density, you cannot say anything without more
information (assuming the oak trees also follow a Poisson). No amount of
messing about with ranks, means, sds, or anything else will reveal how many
non-oak trees there are.

Graham Jones





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