Dear Colleagues
I would like to have some comments on this important topic.
The problem somehow concerns with variance calculation. In any flavor of
(co)kriging, estimated value of Y at spatial location x_0 can be
considered as linear combination of observations. If variogram increases
upon increase in separation distance, then that linear combination has to
be an admissible linear combination for Y(x_0) to have finite variance.
For a linear combination to be an admissible one, the sum of coefficients
has to be zero. You can use ordinary kriging for both stationary and
nonstationary random function. Look at the following propositions when
comparing these two concepts:
1. For a stationary RF, kriging system can be written in terms of both
covariance and/or variogram functions. However, as constant mean is not
given, expressions in terms of variogram function is preferred.
2. For a nonstationary RF, kriging system CANNOT be written in terms of
covariance function as it is not defined according to one school of
thoughts. It has to be written in terms of variogram function. That is
where the problem will arise. Implementing two well-known conditions
(i.e., unbiasedness and minimum variance conditions) on residuals will
lead to an expression in terms of covariance which is not defined. Hence,
by proper means, one has to get rid of covariance computation. That is
where the notion of incrementing and admissible linear combination and
consequently intrinsic hypothesis will come into consideration in order to
express variance of residual in terms of variogram. See, implementing
ordinary kriging on both stationary and nonstationary RF has to be
written in terms of variogram for different reasons.
There is an interesting comparison between stationary RF and Intrinsic RF
model in Kitanidis, Introduction to Geostatistics, page 53 which could
be read.
Thanks
Abedini
On Mon, 28 Aug 2006, [EMAIL PROTECTED] wrote:
Do stationary hypothesis variograms have a sill,
and intrisic hypothesis variograms have no sill.
Does this mean intrisic hypothesis variograms
indicate a trend.
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