AI-GEOSTATS: Re: pseudo cross variogram: h=0

[Isobel Clark]

Peijun

 

That is interesting to hear. I wish you luck in its use. If you are writing any reports, you may wish to refer to our original paper "A novel approach to co-kriging" published in the 1980s and downloadable from my personal site at http://uk.geocities.com/drisobelclark/resume (follow publications link).

 

Isobel

Peijun Li <[EMAIL PROTECTED]> wrote:

Dear Dr. Clark,

 

Thank you for reply.

You know that any point (i.e. pixel) in an image has a value (graylevel value), which is different from sparsely sampling data in geosciences.

We use the pseudo cross variogram to characterize the spatial cross correlation between two variables.

 

Peijun

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From: Isobel Clark [mailto:[EMAIL PROTECTED]
Sent: Thursday, September 21, 2006 10:28 PM
To: Peijun Li
Cc: ai-geostats@jrc.it
Subject: RE: pseudo cross variogram: h=0

 

Peijun

 

I presume by the "pseudo" cross semi-variogram, you mean the 'non co-located' cross semi-variogram as opposed to the more traditional co-located cross semi-variogram?

 

If so, the difference between the sill of your model and the nugget effect at zero is simply the classical covariance between your two variables. This is one way to calculate the covariance or correlation when you do not have co-located data for a more traditional statical calculation.

 

Interestingly, this cross semi-variogram is the only one which actually takes a non-zero value at zero distance!

 

Personally, I dislike the term "pseudo" which suggests that this is some sort of approximation to the "real" thing. Both approaches to co-kriging have strengths and weaknesses. So long as you are aware of these, you can gain valuable insight into your cross-relationships.

 

Isobel

http://www.kriging.com

Peijun Li <[EMAIL PROTECTED]> wrote:

Dear Dr. Goovaerts,



Thanks for reply.

I compute the pseudo cross variogram from bi-temporal images for change
detection. I found that when lag h=0, the pseudo cross variogram image
obtained highlights the change in the image. So, I would like to understand
why it happens.



Peijun





Peijun Li

Institute of Remote Sensing and GIS

Peking University, Beijing 100871

P R China





_____

From: Pierre Goovaerts [mailto:[EMAIL PROTECTED]
Sent: Thursday, September 21, 2006 2:15 AM
To: Peijun Li; ai-geostats@jrc.it
Subject: RE: AI-GEOSTATS: pseudo cross variogram: h=0



Hi,



It just represents half the average squared difference between the values of
the two variables

measured at the same location.. I don't know why you compute the pseudo
cross-variogram

but, personally, I don't like this statistic, mainly because of the lack of
interpretation...

for example, it cannot take negative values, hence you can't differentiate

between positive and negative correlations. It is useful mainly when the two
variables have

not been measured at the same locations.



Pierre



Pierre Goovaerts

Chief Scientist at BioMedware Inc.

Courtesy Associate Professor, University of Florida

President of PGeostat LLC



Office address:

516 North State Street

Ann Arbor, MI 48104

Voice: (734) 913-1098 (ext. 8)
Fax: (734) 913-2201

http://home.comcast.net/~goovaerts/



_____

From: owner-ai-geostats@jrc.it on behalf of Peijun Li
Sent: Wed 9/20/2006 12:35 PM
To: ai-geostats@jrc.it
Subject: AI-GEOSTATS: pseudo cross variogram: h=0

Dear List,



I recently use the pseudo cross variogram (PCV) for remote sensing
applications. However, I don't know what does the PCV reflect when lag h=0?
As we know, when lag h=0, the (univariate) variogram reflects the nugget
effect. Is there any similar meaning for PCV? Could you give me some
references related to PCV?



Thanks in advance for reply.



Peijun Li

Peking University