Hi,
I like the question too.
The statement that weights for points beyond the variogram range get
zero weight is true for simple kriging, but not for ordinary and
universal/ext.drift kriging; I think this hint is sufficient to find out
why.
The statement that local kriging is always faster than global is also
not always true; for global kriging you have to decompose the covariance
matrix only once, and back solve for each prediction, for local kriging
you have to decompose (a smaller system) at each prediction location.
The decomposition is the most expensive part, O(n^2), whereas back
substitution is O(n) with n the neighbourhood size. Also, neighbourhood
selection can, depending on the strategy (smart indexing?) used, be more
or less expensive.
I tend to use all data if the total is less than say 1000; another
(disputable) issue is that in this case you have to explain less. I must
admit that this is usually in a universal kriging (aka ext.drift)
setting, where trend estimates can go wild in case of small neighbourhoods.
I did an extensive neighbouhood size ,cross validation excercise for
SIC2004, using ordinary kriging, and it turned out to be a factor of
little imporatance (I recall that there was an optimum for this data set
at n=125).
--
Edzer
Ashton Shortridge wrote:
I like this question.
The more points you use, presumably the better the estimation will be. In
practice however, the influence of distant observations, especially with
intervening closer observations, is very slight. Computationally the solution
grows much more complex as the number of observations is increased. It's more
efficient to solve many many small systems (n=4 closest points) than one
global system (n=all points), for example.
I don't think there is any reason to include points more distant than the
range of your covariance structure(s), as those observations won't have any
weight.
Personally, I tend to use between 8 and 16 points, but others with more
experience may employ more. I'm probably just more impatient for results!
Yours,
Ashton
On Friday 30 June 2006 10:43 am, Alí Santacruz wrote:
Dear list members,
I have a very simple question (I think):
When I want to perform a kriging, I must define the number of nearest
observations that should be used for the kriging prediction, or a maximum
distance from the prediction location.
What criteria should I use to set these parameters? Which is the optimum
number of nearest neighbors?
Any comment is welcome.
Sincerely,
Alí M. Santacruz
M.Sc. Geomatics, Student
National University of Colombia
Bogotá D.C.
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