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[ai-geostats] modelling trend and kriging type

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  • Recep kantarci
    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
    Message 1 of 10 , Jun 30, 2005
      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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    • Edzer J. Pebesma
      ... I believe not. There s a fourth term, kriging with external drift , which also is the same, in my view. Some people may like to distinguish the case where
      Message 2 of 10 , Jun 30, 2005
        Recep kantarci wrote:
        > 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?
        >
        I believe not. There's a fourth term, "kriging with external drift",
        which also is the same, in my view. Some people may like to distinguish
        the case where external variables are (powers of) coordinates or not,
        but mathematically it's all identical.

        If we were to choose a name now, maybe I would prefer "regression
        kriging", but being the (newest) fourth name for an old technique, I
        don't like it. We also stick to "simple" and "ordinary" kriging.

        There's also the other issue of doing regression and
        residual kriging separately and adding the results, which may be
        coined regression kriging.
        --
        Edzer
      • Gregoire Dubois
        Dear Recep, I don t think the type of variable has any impact on the choice of the detrending algorithm. There is indeed a whole collection of methods and one
        Message 3 of 10 , Jun 30, 2005
          Dear Recep,

          I don't think the type of variable has any impact on the choice of the
          detrending algorithm. There is indeed a whole collection of methods and
          one can also cite the various methods in which the trend is modelled by
          neural networks (e.g. Kanevski's NNRK Neural Network Residual Kriging).
          NN can be very useful for complex detrending but less, in my eyes at
          least, if you want to understand the mathematical/physical expression of
          your drift. If you do care, then I would propose to use more simple
          polynomial functions that may be more easy to understand when analysing
          the drift.

          You may find the following report useful

          Hengl, T., Heuvelink, G.B.M. and Stein, A., 2003. Comparison of kriging
          with external drift and regression-kriging. Technical report,
          International Institute for Geo-information Science and Earth
          Observation (ITC), Enschede, pp. 18.
          http://www.itc.nl/library/Papers_2003/misca/hengl_comparison.pdf

          The first author has also on the web a practical guide to
          regression-kriging explaining how to do it with various software. See
          http://hengl.pfos.hr/RKguide.php

          Hope this helps,

          Gregoire

          -----Original Message-----
          From: Recep kantarci [mailto:recep_kantarci_1978@...]
          Sent: 30 June 2005 15:39
          To: ai-geostats@...
          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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        • Pierre Goovaerts
          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
          Message 4 of 10 , Jun 30, 2005
            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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            Istenmeyen postadan biktiniz mi? Istenmeyen postadan en iyi korunma Yahoo! Posta’da
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          • Els Verfaillie
            Dear AI-list, in which context KED is mostly used? I have found examples of this methodology in the context of soil science and climatology: Bourennane, H.,
            Message 5 of 10 , Jul 1, 2005
              Dear AI-list,

              in which context KED is mostly used? I have found examples of this methodology in the context of soil science and climatology:


              Bourennane, H., King, D. and Couturier, A., 2000. Comparison of kriging with external drift and simple linear regression for predicting soil horizon thickness with different sample densities: Geoderma, v. 97, p. 255-271.

              Bourennane, H. and King, D., 2003. Using multiple external drifts to estimate a soil variable: Geoderma, v. 114, p. 1-18.

              Goovaerts, P., 1999. Using elevation to aid the geostatistical mapping of rainfall erosivity: Catena, v. 34, p. 227-242.

              Hudson, G. and Wackernagel, H., 1994. Mapping temperature using kriging with external drift: theory and an example from Scotland: International Journal of Climatology, v. 14, p. 77-91.

              Martinez-Cob, A. and Cuenca, R.H., 1992. Influence of elevation on regional evapotranspiration using multivariate geostatistics for various climatic regimes in Oregon. Journal of Hydrology 136, 353–380.


              Are there other interesting references for this methodology in the same or other application fields?

              Best wishes,
              ___________________________________________________

              Els Verfaillie, PhD student
              Renard Centre of Marine Geology - Ghent University
              Krijgslaan 281-S8
              B-9000 Gent - Belgium
              tel: +32-9-2644573 fax: +32-9-2644967
              e-mail: Els.Verfaillie@...
              http://www.rcmg.ugent.be/
              ___________________________________________________


              -----Original Message-----
              From: Pierre Goovaerts [mailto:Goovaerts@...]
              Sent: donderdag 30 juni 2005 16:54
              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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              Istenmeyen postadan biktiniz mi? Istenmeyen postadan en iyi korunma Yahoo! Postada
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            • ABREU Carlos Eduardo
              Dear Els A good reference on geostats in the oil industry is the excelent book from Olivier Dubrule Geostatistics for Seismic Data Integration in Earth
              Message 6 of 10 , Jul 1, 2005
                Dear Els

                A good reference on geostats in the oil industry is the excelent book from
                Olivier Dubrule "Geostatistics for Seismic Data Integration in Earth
                Models", where you will also find KDE aplications.

                Actually, it is the reference book of a 1 day course offered by SEG (Society
                of Exploration GEophysicists)/EAGE (European Association og Geoscientists
                and Engineers).
                http://www.eage.org/index.php?Menu_Code=DISCDetails&EVS_Id=45&ActiveMenu=57&
                Opendivs=s13,s15


                Sincerely

                Carlos Eduardo ABreu

                -----Message d'origine-----
                De : Els Verfaillie [mailto:els.verfaillie@...]
                Envoyé : vendredi 1 juillet 2005 10:55
                À : Pierre Goovaerts; Recep kantarci; ai-geostats@...
                Objet : RE: [ai-geostats] modelling trend and kriging type


                Dear AI-list,

                in which context KED is mostly used? I have found examples of this
                methodology in the context of soil science and climatology:


                Bourennane, H., King, D. and Couturier, A., 2000. Comparison of kriging with
                external drift and simple linear regression for predicting soil horizon
                thickness with different sample densities: Geoderma, v. 97, p. 255-271.

                Bourennane, H. and King, D., 2003. Using multiple external drifts to
                estimate a soil variable: Geoderma, v. 114, p. 1-18.

                Goovaerts, P., 1999. Using elevation to aid the geostatistical mapping of
                rainfall erosivity: Catena, v. 34, p. 227-242.

                Hudson, G. and Wackernagel, H., 1994. Mapping temperature using kriging with
                external drift: theory and an example from Scotland: International Journal
                of Climatology, v. 14, p. 77-91.

                Martinez-Cob, A. and Cuenca, R.H., 1992. Influence of elevation on regional
                evapotranspiration using multivariate geostatistics for various climatic
                regimes in Oregon. Journal of Hydrology 136, 353–380.


                Are there other interesting references for this methodology in the same or
                other application fields?

                Best wishes,
                ___________________________________________________

                Els Verfaillie, PhD student
                Renard Centre of Marine Geology - Ghent University
                Krijgslaan 281-S8
                B-9000 Gent - Belgium
                tel: +32-9-2644573 fax: +32-9-2644967
                e-mail: Els.Verfaillie@...
                http://www.rcmg.ugent.be/
                ___________________________________________________


                -----Original Message-----
                From: Pierre Goovaerts [mailto:Goovaerts@...]
                Sent: donderdag 30 juni 2005 16:54
                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


                _____

                Yahoo! kullaniyor musunuz?
                Istenmeyen postadan biktiniz mi? Istenmeyen postadan en iyi korunma
                Yahoo! Postada
                http://tr.mail.yahoo.com <http://tr.mail.yahoo.com/>


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                Checked by AVG Anti-Virus.
                Version: 7.0.322 / Virus Database: 267.8.2/29 - Release Date: 27/06/2005

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                Checked by AVG Anti-Virus.
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              • PCollier@xstrata.com.au
                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
                Message 7 of 10 , Jul 6, 2005
                  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

                         
                    _____ 

                          Yahoo! kullaniyor musunuz?
                          Istenmeyen postadan biktiniz mi? Istenmeyen postadan en iyi korunma Yahoo! Posta’da
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                  If you receive this e-mail in error, any use, distribution or

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                • Isobel Clark
                  Perry Your basic semi-variogram graph has a parabola added to it. Shoots off upwards (usually) at some distance. If the distance is large (past the range of
                  Message 8 of 10 , Jul 7, 2005
                    Perry
                     
                    Your basic semi-variogram graph has a parabola added to it. Shoots off upwards (usually) at some distance. If the distance is large (past the range of influence) you can ignore it. See some of our  mid-80s papers on the Wolfcamp data which lots of people use as a teaching set now. Or read my free tutorial at http://geoecosse.bizland.com/softwares (kriging with trend).
                     
                    Isobel

                    PCollier@... wrote:

                    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

                           
                      _____ 

                            Yahoo! kullaniyor musunuz?
                            Istenmeyen postadan biktiniz mi? Istenmeyen postadan en iyi korunma Yahoo! Posta’da
                            http://tr.mail.yahoo.com <http://tr.mail.yahoo.com/>

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                    Support Centre phone: Australia 1800 500 646

                    International +61 2 9034 3710

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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 9 of 10 , Jul 7, 2005
                      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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                    • sebastiano.trevisani@unipd.it
                      Dear Perry Collier I`m interested in the second question: what is the difference between a dataset with a trend and a non-stationary dataset? Without clearly
                      Message 10 of 10 , Jul 8, 2005
                        Dear Perry Collier
                        I`m interested in the second question: what is the difference between a dataset
                        with a trend and a non-stationary dataset?
                        Without clearly pointing out about which kind of stationarity we are talking
                        (second order, intrinsic or generalized intrinsic), we need stationarity
                        (well !!! togheter with ergodicity) for some statistical index (in this case a
                        index about spatial variability) to perform inference. From my perspective the
                        dualism trend-residual makes possible always (or not?) to explain non
                        stationarity in spatial variability in term of presence of a trend: this trend
                        could be global as well as local: it is only a matter of scale.The point is: we
                        have reasons or so many data to use a complex trend model?

                        In particular this question makes me to think to a point. Very often people who
                        use Universal Kriging do this:
                        1) detrend data globally (same trend coefficients for all spatial domain)
                        2) calculate a residual variogram
                        3) perfom Uk with local search windows (inside which the trend coefficients are
                        calculated i.e. the trend is filtered locally)
                        This doesen`t seem to me correct: I think (maybe, if you have many data IRF-K
                        approach works better) that you can not
                        one time calculate trend globally and the other time locally: it could happen
                        that globally you need a quadratic trend while locally a linear trend model is
                        enough. What about that?

                        Sincerely,
                        Sebastiano Trevisani



                        At 03.48 07/07/2005, PCollier@... wrote:

                        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


                        _____

                        Yahoo! kullaniyor musunuz?
                        Istenmeyen postadan biktiniz mi? Istenmeyen postadan en iyi korunma
                        Yahoo! Posta’da
                        http://tr.mail.yahoo.com <http://tr.mail.yahoo.com/>

                        **********************************************************************

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                        intended only for the use of the addressee(s).

                        If you receive this e-mail in error, any use, distribution or

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                        forward unwanted e-mail and address any problems to the

                        Xstrata Queensland Support Centre.

                        Support Centre e-mail: supportcentre@...

                        Support Centre phone: Australia 1800 500 646

                        International +61 2 9034 3710

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