- Jun 30, 2005Ciao Simone,

I'm not sure I fully understand your question. Are you referring to the

monomials used to define the stationary trend model of the IRF-k?

What are these coefficients of 1 and -1 ?? I must admit I am very lazy

tonight !

The fundamental differences between IRF-k and UK can be found in part 6

of a paper by Arianna Orasia

http://w3.uniroma1.it/DSPSA/Rapporti_tecnici/orasijonaferrari.pdf

Some readings are:

1) the paper of D. Marcotte, M. David (1988)

Trend surface analysis as a special case of IRF-k kriging,

Mathematical Geology, 20(7): 821 - 824

2) the papers of van den Boogaart (hard reading !!!), e.g.

http://www.math-inf.uni-greifswald.de/~boogaart/Publications/BoogaartPub

lications.html

Why Universal Kriging is better than IRFk-Kriging: Estimation of

Variograms in the Presence of Trend

Karl Gerald van den Boogaart& Alexander Brenning

June 30, 2001

3) If you survived the reading above, then you can always go for a paper

from Alexander Brenning:

http://www.geographie.uni-erlangen.de/abrenning/lit/trend.pdf

4) This one should saves your day (in Italian and easy reading) but it

is probably impossible to find today:

Bruno R. & Raspa G. (1994). La pratica della geostatistica lineare. Il

trattamento

dei dati spaziali. Guerini Studio. 170 p

The book is all about FAIK (Italian equivalent to IRFk) and has (had?)

an MS DOS software for FAIK, FAIPACK, that was not bad at all.

There was also a wonderful text from Chauvet that I could try to find

again if needed but it is in French (try to contact Fontainebleau).

Chiles and Delfiner probably discuss this as well in their book but I

don't have it here.

For what concerns the previous mail regarding trend modelling, IRF-k can

be nicely automated for detecting the optimal "k" but I would make the

same critic as for the Neural Nets, you do not extract any useful

information from the drift (although you could map the local values of

k.. allowing you so to describe somehow the complexity of the underlying

trend.. Don't know if this has been done or any useful).

Cheers,

GD

PS: there are some nice papers from Chauvet (Fontainebleau) that I could

try to find again if needed but there are in French.

Chiles and Delfiner probably discuss this in their book but I don't have

it here.

-----Original Message-----

From: Simone Sammartino [mailto:marenostrum@...]

Sent: 29 June 2005 17:49

To: Geostat newsgroup

Subject: [ai-geostats] Irf-k theory...

Dear all

about Irf-k...

I can't understand the link between the two approach explaining the

Irf-k theory... 1st approach: The Irf-k approach is based on a

generalization of the intrinsic model, in which the coefficients of the

combination of the variables in the X points are such that the

combination of monomials of the variables (computed with such

coefficients) is zero mean and second order stationary. In the intrinsic

model the coefficients are 1 and -1 and the linear combination of the

variables with such coefficients (the increment) is second order

stationary. Now...how to insert the generalized covariance in this

speech?... 2nd approach:

The non stationary random function is seen as the sum of a trend and a

residual (as in UK?!)...such trend is the linear combination of

monomials of the variables (as in UK?!) with the said coefficients. And

the generalized covariance? Reassuming...I did not understand the Irf-K

theory...

Someone can explain it to me? or suggest some clear refer? Thank you

Simone

-----------------------------

Dr. Simone Sammartino

PhD student

- Geostatistical analyst

- G.I.S. mapping

I.A.M.C. - C.N.R.

Geomare-Sud section

Port of Naples - Naples

marenostrum@...

-----------------------------

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