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RE: [ai-geostats] modelling trend and kriging type

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  • Gregoire Dubois
    Hi Perry, I am curious to see how others will reply to your second question on the difference between a dataset with a trend and one that is non-stationary! My
    Message 1 of 10 , Jul 7, 2005
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      Hi Perry,

      I am curious to see how others will reply to your second question on the
      difference between a dataset with a trend and one that is
      non-stationary! My reply may sound provocative: you can always remove a
      trend when you recognize that there is one. Moving from non-stationarity
      to stationarity, on the other hand, can be infinitely more complex (e.g.
      moving to non-Euclidean space)

      :)


      For what concerns the detection of trends, have a look at the variogram:
      a quadratic/exp. increase usually means that there is a trend. Get rid
      of the presumed trend and check the variogram of the residuals which
      should clearly show a change of structure (if you had a trend
      obviously). Quicker might be to use a moving windows strategy to plot
      local averages and check if you see any structure (be careful that the
      "structure" is not simply an anisotropy of your variable). You could
      have a look into the old archives of AI-GEOSTATS. There have been very
      nice replies from Donald Myers (see his publications) in the past on
      these issues. see http://groups.yahoo.com/group/ai-geostats/

      Regards

      GD



      -----Original Message-----
      From: PCollier@... [mailto:PCollier@...]
      Sent: 07 July 2005 03:49
      To: ai-geostats@...
      Subject: RE: [ai-geostats] modelling trend and kriging type


      Hi all
      I may know this already, but what are the symptoms of data with a trend?
      What is the difference between a dataset with a trend and a
      non-stationary dataset?
      Cheers


      Perry Collier
      Senior Mine Geologist
      Ernest Henry Mine
      Xstrata Copper Australia
      Ph (07) 4769 4527
      Fx (07) 4769 4555
      E-mail PCollier@...
      Web http://www.xstrata.com

      PO Box 527
      Cloncurry QLD 4824
      Australia

      "Light travels faster than sound. That is why some people appear bright
      until you hear them speak"




      -----Original Message-----
      From: Pierre Goovaerts [mailto:Goovaerts@...]
      Sent: Friday, 1 July 2005 12:54 AM
      To: Recep kantarci; ai-geostats@...
      Subject: RE: [ai-geostats] modelling trend and kriging type


      To add to the excellent comments by Edzer and Gregoire,

      1. Universal kriging = kriging with a trend. The second terminology has
      been proposed by Andre
      Journel who felt that the term "universal" was vague and misleadingly
      "ambitious".

      2. Kriging with an external drift (KED) is mathematically the same as
      universal kriging (UK). Secondary variables
      are simply replacing the spatial coordinates used in UK.

      3. Regression kriging denotes all the techniques where the trend is
      modeled outside the kriging algorithm.
      There are various methods that can be used to model that trend, ranging
      from linear regression
      to neural networks. Kriging is used to interpolate the residuals. In
      practice these techniques have more
      flexibility than universal kriging in term of modeling the trend:
      multiple variables either categorical or
      continuous can be incorporated easily and many sofwtare are available
      for this trend modeling.
      The only limitation is that the trend is modeled globally (i.e. the
      regression coefficients are constant
      in space) while in KED the coefficients are reestimated within each
      search window.

      Cheers,

      Pierre

      Pierre Goovaerts
      Chief Scientist at Biomedware
      516 North State Street
      Ann Arbor, MI 48104
      Voice: (734) 913-1098
      Fax: (734) 913-2201
      http://home.comcast.net/~goovaerts/
      -----Original Message-----
      From: Recep kantarci [mailto:recep_kantarci_1978@...]
      Sent: Thu 6/30/2005 9:38 AM
      To: ai-geostats@...
      Cc:
      Subject: [ai-geostats] modelling trend and kriging type


      Dear ai-geostats members

      When the data used has a trend, it is needed to model trend and
      in this case there exists various types of kriging to apply (universal
      kriging, kriging with a trend, regression kriging etc).
      If this is the case, does one should use the same type of
      kriging or different depending on modeling the trend using coordinates
      of target variable or using other (namely, secondary or auxillary)
      variables such as elevation or topography ? That is , are there a
      dinstinction depending on the type of variables to model the trend while
      kriging?

      Best regards
      Recep

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