## AI-GEOSTATS: Regression slope in kriging

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• Dear ai-geostat follows I have some questions regarding kriging. 1.Kriging is often cited as least squares regression method - this I understand for liner
Message 1 of 3 , Apr 28, 2003
Dear ai-geostat follows

I have some questions regarding kriging.

1.Kriging is often cited as least squares regression method - this I
understand for liner regression but how does this actually occur in the
kriging matrix ? Are the covariances the square values that are being
minimised ?

2.I read in seveal papers that it is possible to calculate the slope of
regression from parameters of the krigin system. Specifically:

(Block variance-kriging variance + abs(lagrangian))/(block varaince -
kriging variance + 2 x abs(lagrangian))

I can follow the derivation of the kriging variance and I can see the
purpose of the lagrangian, where does the block variance come from and how
(in conceptual terms) does this equation give the regression slope of true

Joe

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• Joe ... Simple kriging as invented by Danie Krige in the 1950 s was exactly a linear regression method. The kriging system has a left-hand-side consisting
Message 2 of 3 , Apr 29, 2003
Joe

> 1.Kriging is often cited as least squares regression
Simple kriging as invented by Danie Krige in the
1950's was exactly a linear regression method. The
'kriging' system has a 'left-hand-side' consisting of
the variance/co-variance matrix between sample pairs
and a 'right-hand-side' consisting of the co-variances
between each sample and the unknown value. Krige
derived the variances and co-variances empirically
from 50 years of historical data.

In the early 1960s, Matheron's work put this on a
modelling (theoretical) footing by suggesting that the
co-cariances could be modelled by a function -- the
semi-variogram reversed. Thus the l.h.s became
co-variances or semi-variograms depending on your
personal preference and likewise the r.h.s.

However, Matheron also introduced the notion that the
weights should add up to one and invented 'ordinary'
kriging which is not (strictly) classical linear
regression.

> 2.I read in seveal papers that it is possible to
> calculate the slope of
> regression from parameters of the krigin system.
All explained in my 1983 paper 'regression revisited'
in Mathematical Geology. I can send you a copy if you

http://uk.geocities.com/drisobelclark/resume/Publications.html

(note capital P)

Isobel Clark
http://geoecosse.bizland.com/whatsnew.htm

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• Joe, What is the formulae for the regression slope for punctual kriging, you only cited the case for block kriging. By block variance do you mean the
Message 3 of 3 , Apr 29, 2003
Joe,
What is the formulae for the regression slope for punctual kriging,
you only cited the case for block kriging. By block variance do you
mean the dispersion variance of points within blocks or the distribution