Dear list : Following the intuition of Roderik Lindenbergh, I would actually like to ask as question to the whole list whether :
"The positive definiteness between a set of points, as needed for kriging, is not spoiled by changing the distance metric between these points, as long as one uses a valid distance metric as defined for example in http://mathworld.wolfram.com/Metric.html"; ? Note that the above statement refers to the positive-definiteness needed for kriging, not the merely positive-definiteness of a covariance model. I am not sure which of these was Roderik refering to. I don't think that everybody would agree with the above statement, but what work exists either proving it, or providing counter examples? Marc Serre Assistant Professor, Environmental Sciences and Engineering The University of North Carolina at Chapel Hill Chapel Hill, NC 27599-7431, USA ----- Original Message ----- From: "Roderik Lindenbergh" <[EMAIL PROTECTED]> To: <[email protected]> Sent: Friday, April 06, 2007 3:16 PM Subject: Re: AI-GEOSTATS: Kriging a non-planar surface lacking natural parametization Dear list, my intuition is that as long as you define a valid notion of distance on the object of interest, in this case a bone, you can do Kriging. The idea is that the variogram/covariance function does not `know` how your point pair distance is obtained anyway, so the positive definiteness is not spoiled by changing your distance function. A valid notion of distance is obtained by making sure that your distance function fulfills the requirement of a metric: http://mathworld.wolfram.com/Metric.html that is, triangle inequality should hold, etc. good luck, Roderik Lindenbergh _________________________________________________________________ Wil jij MSN reporter zijn? Deel jouw nieuws en verhalen hier! http://reporter.msn.nl/ + + To post a message to the list, send it to [email protected] + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/ + + To post a message to the list, send it to [email protected] + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
