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

[Digby Millikan]

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" <[EMAIL PROTECTED]>
To: "Geostat newsgroup" <ai-geostats@unil.ch>; "Simone Sammartino" 
<[EMAIL PROTECTED]>
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


--------------------------------------------------------------------------------

* By using the ai-geostats mailing list you agree to follow its rules
( see http://www.ai-geostats.org/help_ai-geostats.htm )
* To unsubscribe to ai-geostats, send the following in the subject or in 
the body (plain text format) of an email message to [EMAIL PROTECTED]

Signoff ai-geostats 


* By using the ai-geostats mailing list you agree to follow its rules 
( see http://www.ai-geostats.org/help_ai-geostats.htm )
* To unsubscribe to ai-geostats, send the following in the subject or in the 
body (plain text format) of an email message to [EMAIL PROTECTED]

Signoff ai-geostats