Hi Pierre
Welcome back to the discussion.
I don't use simple kriging, except as a teaching
exercise on the way to ordinary kriging. However, it
is very commonly used in Africa and other parts of the
world. In particular, some major mining houses in
Southern Africa use a combination of the de Wijsian
semi-variogram model (which is unbounded) and simple
kriging. Since these people were trained by Danie
Krige, and he wrote a book about it way back in 1979,
I have to assume that it is well founded.
> On page 65 of Gslib user manual, 2nd paragraph, I
> quote:
> "In the sytem (IV.4) (SIMPLE kriging system!), the
> covariance values C(h) cannot be replaced by
> semivariogram values
> g(h)=C(O)-C(h) unless sum_lambda = 1, which is the
> ordinary kriging constraint". I guess it's clear
> enough, and that is nothing to do with whether we
> should solve an ordinary
> kriging system in terms of covariances or
> semivariograms
> (Everybody knows that you get the same results!), or
> whether we should teach students in one way or
> another...
Well, gosh, I am not arguing about whether you can
replace the covariance with the semi-variogram. I
thought we were discussing replacing the
semi-variogram with the covariance. But here goes:
In simple kriging the weights do not necessarily sum
to one. The 'rest' of the weight is given to the
regional mean. If the weights do not sum to one, when
you replace the covariance by the semi-variogram (or
vice versa) you have (1-sum of weights) times variance
left over. That variance is the variance of the sample
values around the regional mean. The term (1-sum of
weights) is the weight accorded to the regional mean.
Hence the variance supposedly 'left over' is actually
accounted for by the regoinal mean term.
In simple kriging, the weights do sum to one -- it is
just that some of it is on the regional mean and not
the individual samples.
> Given that SIMPLE kriging is rarely used, we might
> even
> argue that all this discussion is pointless...
I could be rude and describe this view as parochial,
but I won't do that. Striken from the record.
> Again, the reason for that e-mail is to clarify the
> matter
> for students or practitioners who might have been
> confused by this exchange of e-mails... I don't have
> a book, a software or a consulting company to
> advertise!
Oh dear, oh dear. Let's be petty. You do so have a
book and I have a copy.
Isobel
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