Hi Paul
Well, in some way regression kriging is not too
much different to kriging with external drift.
My question is more directed to kernel smoothing
techniques than to classical geostatistical tools.
I should have read the mentioned paper some time
ago...I'll go to give another look.
Sebastiano
At 13.56 02/02/2010, you wrote:
Cornford, Dan wrote:
Sebastiano,
I am struggling to understand why you are
interested in doing trend + residual
separation? There can be no unique
decomposition of a data set into trend and
residual, it is a judgement about what model
you feel is most appropriate given your prior
beliefs and observations (evidence). The only
thing you can say about the model is to
validate it on out of sample data (even as a
Bayesian I say this!). So in a sense there is
no correct decomposition, and any decomposition
is valid (so long as it is correctly
implemented maybe that is your question?).
Are some decompositions better than others?
Well yes they are likely to be, but this
largely depends on your data (and the completeness of the overall model).
An article by Tomislav Hengl goes into
separately estimating the trend and then
interpolating the residuals [1]. He calls it
regression kriging. Might be interesting to have
a look at it in light of this discussion.
cheers,
Paul
[1] http://dx.doi.org/10.1016/j.cageo.2007.05.001
@ARTICLE{Hengl2007,
author = {Hengl, T. and Heuvelink, G.B.M. and Rossiter, D.G.},
title = {About regression-kriging: From equations to case studies},
journal = {Computers \& Geosciences},
year = {2007},
volume = {33},
pages = {1301--1315},
number = {10},
}
In terms of your original question about the
shape of the kernel there is no overall theory
that I am aware of different kernels will
have different properties in terms of the
function classes that they represent (e.g.
differentiability, frequency response /
characteristic length scales). Kernel families
will have different null spaces which might or
might not be important for your specific
application and what you want to find out.
Im not sure if this is terribly helpful
but
I think it is the reality everything depends
on your data and your judgement (prior).
Conditional on those you get a model and you
need to validate this model carefully
then you are OK.
cheers
Dan
-------------------------------------------
Dr Dan Cornford
Senior Lecturer, Computer Science and NCRG
Aston University, Birmingham B4 7ET
www: http://wiki.aston.ac.uk/DanCornford/
tel: +44 (0)121 204 3451
mob: 07766344953
-------------------------------------------
------------------------------------------------------------------------
*From:* owner-ai-geost...@jrc.ec.europa.eu
[mailto:owner-ai-geost...@jrc.ec.europa.eu] *On Behalf Of *seba
*Sent:* 02 February 2010 08:39
*To:* Pierre Goovaerts
*Cc:* ai-geostats@jrc.it
*Subject:* Re: AI-GEOSTATS: moving averages and trend
Hi Pierre
I think that for my task factorial kriging is a little bit
too much sophisticated (nevertheless, is there any open source or
free implementation of it ??? I remember that
it is implemented in Isatis.....).
I have an exhaustive and regularly spaced data set (i.e. a grid) and I need
to calculate locally the spatial variability of
the residual surface or better
I would like to calculate the spatial
variability of the high frequency component.
Here I'm lucky because I know exactly what I
want to see and what I need to filter out.
In theory, using (overlapping) moving window
averages (but here it seems better to use some more complex kernel)
one should be able to filter out the short
range variability (characterized by an eventual
variogram range within the window size???).
Seeing the problem from another perspective, in the case of a perfect
sine wave behavior, I should be able to filter out spatial
variability components with wave lengths up to the window size.
But maybe there is something flawed in my
reasoning....so feedback is appreciated!
Bye
Sebastiano
At 16.27 01/02/2010, you wrote:
well Factorial Kriging Analysis allows you to tailor the filtering weights
to the spatial patterns in your data. You can use the same filter size but
different kriging weights depending on whether you want to estimate
the local or regional scales of variability.
Pierre
2010/2/1 seba < sebastiano.trevis...@libero.it
<mailto:sebastiano.trevis...@libero.it>>
Hi José
Thank you for the interesting references. I'm going to give a look!
Bye
Sebastiano
At 15.46 01/02/2010, José M. Blanco Moreno wrote:
Hello again,
I am not a mathematician, so I never worried
too much on the theoretical reasons. You may be
able to find some discussion on this subject in
Eubank, R.L. 1999. Nonparametric Regression and
Spline Smoothing, 2a ed. M. Dekker, New York.
You may be also interested on searching
information in and related to (perhaps citing)
this work: Altman, N. 1990. Kernel smoothing of
data with correlated errors. Journal of the
American Statistical Association, 85: 749-759.
En/na seba ha escrit:
Hi José
Thank you for your reply.
Effectively I'm trying to figure out the theoretical reasons for their use.
Bye
Sebas
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