I agree with You.
Suppose that ordinary kriging predicts that I am a dwarf (or giant)
with the height H.
Since for e.g. gaussian distribution holds
P(H)=0
we have to introduce
P(H - s < h < H + s) = p
where s is a square root of kriging variance and p is an area under
the gaussian curve for the interval (H-s,H+s) in its tail.
Knowing a total area under the curve we can compute probability.
No matter, am I a dwarf or not, the probability of being a dwarf
(with some height tolerance) is not high so kriging variance will
be small (it means that predicted value "comes from" the tail of
distribution not that estimation is "good").
Prediction intervals have no meaning.
Suppose that ordinary kriging predicts that I have a mean height.
Now, kriging variance (minimized error variance) is the estimator of
variance of random variable (sigma^2) and reaches maximum.
Probability that I have a mean height +/- sigma is high and known
but it is only property of distribution of random variable.
Any prediction intervals have no meaning too.
Best Regards
tom
Want to be your own boss? Learn how on Yahoo! Small Business.
