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Re: AI-GEOSTATS: Block size - estimation variance - resource category.

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• ... Hi Bill It is possible for the kriging variance to be higher than the total sill of the semi-variogram. This total sill is (theoretically) equal to the
Message 1 of 1 , Mar 16, 2001
--- William Thayer <thayer@...> wrote: >
Isobel:
> Would you mind expanding a little on your earlier
> reply? In particular,
> what do you mean by (1) "kriging variance less than
> ordinary
> >statistical sample variance", (2) "not measured but
> within the range
> >of influence of at least 4 samples" and (3)
> "indicated is within range but
> >the local average is a better estimator than the
> kriging"?
>
> Thanks in advance,
> Bill

Hi Bill

It is possible for the kriging variance to be higher
than the total sill of the semi-variogram. This total
sill is (theoretically) equal to the Normal population
variance if your data is (a) stationary and (b)
Normal. For lognormals use logarithms. Or transform
data to Normal scores before calculating
semi-variogram.

For example: if you estimate a point location from a
single sample just below the range of influence away,
the kriging variance is twice the total sill (unless
you follow the Stanford school, in which case it is
twice the total sill minus twice the nugget effect).

Now, if the kriging variance is higher than the
'sample' variance, it means that the population mean
(if you knew it) would be a better estimator than the
local kriging estimate.

So even if you have samples within the range of
influence, you could still get an estimate which has
worse confidence than the regional average. This I
call "indicated". I'm sure it is there but I can't put
a local value on it.

If the kriging variance is less than the total sill
(suitably modified for non-point support), then one
can assign a 'local' value which is better than the
regional average. I consider this "measured".

Anything outside the range of influence is speculative
and the province of the geologist. I am a mining
engineer and don't do "inferred".

Does this help?
Isobel
http://uk.geocities.com/drisobelclark

PS: I have fond memories of Syracuse. Spent the summer
of '76 as visiting prof in geology.

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