• ## Re: [ai-geostats] ...how to distinguish different form of stationarity...

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• Common practice in mining, regions of constant mean and variance are divided up into seperate regions for variogram computation and modelling. ... From:
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Common practice in mining, regions of constant mean and variance are
divided up into seperate regions for variogram computation and modelling.

----- Original Message -----
From: "sl23349" <slin@...>
To: "Geostat newsgroup" <ai-geostats@...>; "Simone Sammartino"
<marenostrum@...>
Sent: Thursday, May 12, 2005 1:55 AM
Subject: RE: [ai-geostats] ...how to distinguish different form of
stationarity...

> Simone,
>
>
> My understanding of Intrinsic Hypothesis is that it is based on the
> stationarity of both difference (1st order) and variance of difference
> (2nd
> order). So the statement your wrote " Intrinsic hypothesis is different
> from
> second order one mainly because in the first case covariance function does
> not
> exist and variogram is computed instead of it...." does not make sense to
> me.
>
>
>>The problem is how to realize about the intrinsicness of my
>>variable...what
>>does "covariance does not exist" mean?...I can calculate covariance with
> ISATIS >and when variogram increases not bounding around a priori variance
> my
>>covariance will be negative...but it continue to exist!....so how to
>>distinguish second order from intrinsic variables?....and decide if beeing
> able >to use only variogram or choose between covariance or variogram?....
>
> There is a trick in the relationship between "stationarity" and "existing
> of
> variogram". Here is my logic,
>
> (1) When there is stationarity of both 1st and 2nd order, the
> semivariogram
> exists. On the other hand, (2) If there is semivariogrm exists, does that
> mean
> the stationarity of both 1st and 2nd order exist? Intrinsicness Theory is
> based on ideal situation I can not totally agree after some simulation I
> have
> done. The first case prevails, but not the second case.
>
> When you have second order, or covariance, non-stationarity, it does not
> mean
> the covariance not exising. Rather, it means the variation is too large
> and
> the 2nd order stationarity does not exist. The 2nd order stationarity is
> also
> called homoskedasticity, while non-stationarity is heteroskedasticity
> (Check
> out http://www.riskglossary.com/articles/heteroskedasticity.htm)
>
> There are two ways we can salvage 2nd order non-stationarity in my
> opinion:
>
> First is about scale. If the study area is large and contains many data,
> instead of using the whole area, conduct some cluster analysis and break
> the
> area into smaller scale areas, each of which may abide by intrinsic
> hypothesis. This means you will get semivariograms on each sub-region of
> the
> whole study area.
>
> Second way is about transforamtion. If the data is limited or the study
> area
> is small, conduct some standardized transformation of data so the
> covariance
> will become stationary.
>
> Hope this helps.
>
>
>
> Shing
>
> Shing-Tzong Lin
> Teaching and Research Assistant
> Department of Geography
> Texas State University, San Marcos
> (512)245-1935
>
>
>

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