- 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

versus actual block grades ?

Thanks in advance

Joe

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> 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

All explained in my 1983 paper 'regression revisited'

> calculate the slope of

> regression from parameters of the krigin system.

in Mathematical Geology. I can send you a copy if you

can't find it or you can download it from:

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

(note capital P)

Isobel Clark

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

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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

variance of block grades.

Digby

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