Dear List
Let us consider theoretical model of stationary random function
with some correlation function.
Model and correlation function are out of any doubts.
First generation of outcome values does not have to cover
the second and go on.
It means that "true" outcome value from first generation
at some coordinate does not have to cover the "true" outcome
value from second generation at the same coordinate and go on.
In practice we see and try to estimate only one generation.
In model point of view we should rather to express
kriging variance by
a) var( estimate(x)-Z'(x) ) where Z' can generate all outcome values
of random variable at some coordinate x
not by
b) var( estimate(x)-Z(x) ) where Z generates only one
"true" outcome value
at some coordinate x
I see that 1.96 catches 95% of probability in case b but not in a
(except mean estimation in case a).
My thesis (right side of kriging variance does not lie):
a) In statistics we have the variance E{ [E{V}-V ]^2 } where E{V} is
expected VALUE and V is random VARIABLE
b) Kriging variance in fact is E{ [S{V}-V]^2 } where S{V} is spread VALUE
and V is random VARIABLE
c) IF S{V} = E{V} then E{ [S{V}-V]^2 } = E{ [E{V}-V]^2 } = sigma^2
IF S{V} <> E{V} then E{ [S{V}-V]^2 } <> E{ [E{V}-V]^2 } = sigma^2
d) We should forget about kriging variance in the case of interpolation
e) We should analyze our interpolation results out of area of interest
(to not meet known values with default zero value of kriging variance).
If kriging variance is equal to sigma^2 (sigma^2 is a multiplier in the
term of correlation function so we can only analyze variance ratio)
then we know mean value of V.
If kriging variance tends to zero it means that predicted value
"disappears" in the tail of distribution of random variable V.
All considerations follow ordinary kriging variance.
P.S.
Gaussian noise is unpredictable (spread value is unpredictable).
Has only mean and variance. Gaussian noise in linear drift also has
only mean and variance cause detrended gaussian noise in drift
has only
constant mean and variance.
Best Regards
tom
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