After sending the message, I checked the relation and noticed a few missing terms. COV[Y(si),Y(sj)]=E{[Y(si)-m(si)][Y(sj)-m(sj)]}=E{[W(si)][W(sj)]}= COV[W(si),W(sj)] -- With Best Wishes Mohammad J. Abedini Department of Civil and Environmental EngineeringSchool of Engineering, Shiraz UniversityOffice Phone #: Direct: 0711-6474604, Ext.: 0711-(613)3132Cell Phone #: 09173160456 Subject: Inquiry From: Mohammad Abedini <abed...@shirazu.ac.ir> Date: Mon, 06/01/2015 09:38 PM To: ai-geostats@jrc.it
Dear Colleagues It is quite a while where our geo-mailing list is not active and we have to delineate the source of this problem. Anyway, I would greatly appreciate it if I could have your comments and assessment regarding the following issue: Generally speaking, any random function can be written as Y(s)=m(s)+W(s). where m(s)=E[Y(s)]. 1. When m=cte independent of spatial location, then, the covariance of Y at two spatial locations is the same as covariance of W at the same two spatial locations. 2. When m is not constant, a few geostatisticians argue that covariance of Y at two spatial locations cannot be defined and of course it is not equal to covariance of W at the same two locations. 3. I am not quite convinced why covariance of Y at two spatial locations is not defined. I am wondering if this lack of availability is at theoretical level and/or at computational level. Assuming its availability, look at the following mathematical manipulation: COV[Y(si),Y(sj)]=E{[Y(si)-m(si)][Y(sj)-(sj)]}=E{[W(si)][W(sj)]}= COV[W(si),Y(sj)] This implies that the covariance of Y and W is the same. Your critical assessment of the above assertion would be greatly appreciated. -- With Best Wishes Mohammad J. Abedini Department of Civil and Environmental EngineeringSchool of Engineering, Shiraz UniversityOffice Phone #: Direct: 0711-6474604, Ext.: 0711-(613)3132Cell Phone #: 09173160456 >