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[ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW

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  • Seumas P. Rogan
    Hello everyone, I apologize if this question is too elementary for this list; I want to understand the key differences between linear regression, kriging,
    Message 1 of 16 , Dec 31, 2004
      Hello everyone,

      I apologize if this question is too elementary for this list;
      I want to understand the key differences between linear regression,
      kriging, conditional simulation and other interpolation techniques such as
      IDW or splines in the analyses of spatial data. I would like to know the
      assumptions, strengths and weaknesses of each method, and when one method
      should be preferred to another. I browsed the archives and looked at some
      of the on-line papers, but they are written at a level beyond my own
      current understanding. It seems to me that this would be a great topic for
      the first chapter of an introductory spatial analysis textbook. Can anyone
      recommend any basic textbooks or references on this topic?
      Any assistance you can offer would be appreciated.

      Sincerely,

      Seumas Rogan
    • Ben Fang
      Hi: We had participated in AI-GEOSTATS SIC 2004 exercise in the past September. I think that several techniques (Kriging, regression, etc.) may have been used
      Message 2 of 16 , Dec 31, 2004
        Hi:

        We had participated in AI-GEOSTATS SIC 2004 exercise in the past September.
        I think that several techniques (Kriging, regression, etc.) may have been
        used by different participants. It will be illuminating to read the final
        report of SIC 2004 when available.


        K.K. (Benjamin) Fang
        (We had used an interpolant/estimator similar to "IDW" and "nonparametric
        regression".)


        ----- Original Message -----
        From: "Seumas P. Rogan" <sprogan@...>
        To: <ai-geostats@...>
        Sent: Friday, December 31, 2004 11:14 AM
        Subject: [ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW


        >
        > Hello everyone,
        >
        > I apologize if this question is too elementary for this list;
        > I want to understand the key differences between linear regression,
        > kriging, conditional simulation and other interpolation techniques such as
        > IDW or splines in the analyses of spatial data. I would like to know the
        > assumptions, strengths and weaknesses of each method, and when one method
        > should be preferred to another. I browsed the archives and looked at some
        > of the on-line papers, but they are written at a level beyond my own
        > current understanding. It seems to me that this would be a great topic for
        > the first chapter of an introductory spatial analysis textbook. Can anyone
        > recommend any basic textbooks or references on this topic?
        > Any assistance you can offer would be appreciated.
        >
        > Sincerely,
        >
        > Seumas Rogan
        >
        >
        >
        >


        ----------------------------------------------------------------------------
        ----


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      • Digby Millikan
        Seumas Linear regression : not really an estimation technique for spatial data, though regression forms some of the basic theory for the derivation of kriging
        Message 3 of 16 , Jan 1, 2005
          Seumas

          Linear regression : not really an estimation technique for spatial data,
          though regression forms some of the basic
          theory
          for the derivation of kriging equations.
          Splines : not really an estimation technique, just something
          used to make curves smooth on contour plots.
          IDW : after ploygonal technigues the simplest of spatial
          modelling techniques, does not take into
          account
          clustering of data.
          Kriging : a spatial modelling technique superior to IDW
          when you have reasonable variograms, and
          takes into account clustering of data and
          instead
          of using distance to weight samples uses your
          variogram (sometimes referred to as
          statistical distance).
          Conditional simulation: a spatial modelling technique of a special sort.
          Where kriging gives you the "best" estimate.
          Simulation
          is used to analyse other possible outcomes
          for your
          sample set, so you can see the effects if
          reality varies
          from the "best" model. Example use includes
          planning
          for chemical purchases at a metallurgical
          plant, so you
          can plan for variations from your kriged
          model should
          they occur.

          Digby Millikan
          www.users.on.net/~digbym
        • Digby Millikan
          Seumas, Linear regression : not really an estimation technique for spatial data, though regression forms some of the basic theory for the derivation of kriging
          Message 4 of 16 , Jan 1, 2005
            Seumas,

            Linear regression : not really an estimation technique for spatial data,
            though regression forms some of the basic
            theory for the derivation of kriging equations.
            Splines : not really an estimation technique, just something
            used to make curves smooth on contour plots.
            IDW : after polygonal techniques the simplest of spatial
            modelling techniques, does not take into
            account clustering of data.
            Kriging : a spatial modelling technique superior to IDW
            when you have reasonable variograms, and
            takes into account clustering of data and
            instead of using distance to weight samples
            uses your variogram (sometimes referred to
            as statistical distance).
            Conditional simulation: a spatial modelling technique of a special sort.
            Where kriging gives you the "best" estimate.
            Simulation is used to analyse other possible
            outcomes for your sample set, so you can
            see the effects if reality varies from the
            "best" model. Example use includes planning
            for chemical purchases at a metallurgical
            plant, so you can plan for variations from
            your kriged model should they occur.

            Digby Millikan
            www.users.on.net/~digbym
          • Gali Sirkis
            When comparing kriging versus regression, I meant using linear regression between sparse and exhaustive datasets to interpolate the sparse one, since as Digbi
            Message 5 of 16 , Jan 3, 2005
              When comparing kriging versus regression, I meant
              using linear regression between sparse and exhaustive
              datasets to interpolate the sparse one, since as Digbi
              Milligan pointed out in general case regression is not
              an estimation method.

              --- Gali Sirkis <donq20vek@...> wrote:

              > Seumas,
              >
              > see few practical points that you may find useful:
              >
              > 1. kriging vs regression:
              >
              > a) kriging honors original data points, while
              > regression does not
              > b) kriging allows to account for anizotropy
              > c) kriging allows to control the influence of the
              > data
              > points
              >
              > 2. Kriging versus other interpolation technics
              >
              > a) Kriging allows to decluster data
              > b) kriging allows to estimate uncertainty of
              > estimation
              > c) kriging allows to use for estimation secondary
              > information from another exhaustive dataset
              >
              > 3. Kriging vs simulations
              >
              > a) Kriging produces smoother version than real
              > distribution, while simulation gives more details
              > b) simulations allow to estimate joint uncertainty,
              > for example probability that values in several
              > adjacent points are above certain level.
              > c) simulation allows to estimate risk of various
              > scenarios - while kriging only shows the most
              > probable
              > one.
              >
              > All the best,
              >
              > Gali Sirkis.
              >
              >
              > >
              > > Hello everyone,
              > >
              > > I apologize if this question is too elementary for
              > > this list;
              > > I want to understand the key differences between
              > > linear regression,
              > > kriging, conditional simulation and other
              > > interpolation techniques such as
              > > IDW or splines in the analyses of spatial data. I
              > > would like to know the
              > > assumptions, strengths and weaknesses of each
              > > method, and when one method
              > > should be preferred to another. I browsed the
              > > archives and looked at some
              > > of the on-line papers, but they are written at a
              > > level beyond my own
              > > current understanding. It seems to me that this
              > > would be a great topic for
              > > the first chapter of an introductory spatial
              > > analysis textbook. Can anyone
              > > recommend any basic textbooks or references on
              > this
              > > topic?
              > > Any assistance you can offer would be appreciated.
              > >
              > > Sincerely,
              > >
              > > Seumas Rogan
              > >
              > >
              > >
              > > > * By using the ai-geostats mailing list you
              > agree
              > to
              > > follow its rules
              > > ( see
              > > http://www.ai-geostats.org/help_ai-geostats.htm )
              > >
              > > * To unsubscribe to ai-geostats, send the
              > following
              > > in the subject or in the body (plain text format)
              > of
              > > an email message to sympa@...
              > >
              > > Signoff ai-geostats
              >
              >
              >
              >
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            • jyarus
              Hi Seumas: I thought I would throw my 2 cents in regarding a comparison between kriging and linear regression. While some of the responses have hit a few
              Message 6 of 16 , Jan 3, 2005
                Hi Seumas:

                I thought I would throw my 2 cents in regarding a comparison between kriging
                and linear regression.

                While some of the responses have hit a few important differences, like
                Kriging is a spatial estimator and regression is not, or kriging will honor
                the original data and regression will not (unless residuals are added back
                in - not often done). For me, the critical point to be made is between the
                collocated cokriging application and regression. In collocated cokriging,
                like simple regression, two variables are being used, one independent and
                one dependent (of course, this could be expanded to more than one
                independent variable). The object is to predict a value of the dependent
                variable from a relationship established between both the independent and
                dependent observed values. In the ensuing regression equation, there is a
                slope term. For example, in the equation, Y= c-bX, c is the intercept and b
                is the slope. As pointed out by one of the contributors, regression by
                itself is not a spatial estimator, it is a point estimator. As such, the
                equation contains no information about the surrounding data or about the
                relationship between the observed data and the unsampled location where a
                desired estimate of the dependent variable is required. In kriging (or
                cokriging), the slope term "b" is replaced by a covariance matrix that
                informs the system not only about the behavior of the surrounding data
                points and the unsampled location (similar to distance weighting if
                omnidirectional), but also about the spatial behavior within the
                neighborhood - that is, how neighbors are spatially related to other
                neighbors. Thus, the slope term "b" is replaced with a sophisticated
                covariance matrix containing the spatial information.

                The ramifications of using simple regression instead of true spatial
                estimator are significant if the results are presented in map form. While
                this is often difficult to grasp for some, using simple regression as a
                mapping tool will cause geographic portions of a map to consistently be
                overestimated and others underestimated! For example, you may find that all
                the values estimated in the upper left quadrant of the map to be
                overestimated, and those in the lower right to be underestimated. We would
                like to believe that a good spatial estimator will be unbiased, and the
                distribution of the error variances over the area of a map will be uniform -
                no one part of the map will preferentially over- or underestimated. The
                bias brought about by the slope term in simple regression can be easily
                tested and proved.

                I have attached a short paper my partner Richard Chambers and I published in
                the Canadian Recorder a few years back which addressed this issue. The
                article talks about seismic attributes related to petroleum reservoir
                characterization. However, beginning around page 10 or 11, we give an
                example that demonstrates the above points.

                I hope this is informative and useful.

                King Regards,

                Jeffrey M. Yarus
                ------------------------------------
                QGSI
                Jeffrey M. Yarus
                Partner
                jyarus@...
                2900 Wilcrest, Suite 370
                Houston, Texas 77042
                tel: (713) 789-9331
                fax: (713) 789-9318
                mobile: (832) 630-7128
                ------------------------------------

                -----Original Message-----
                From: Seumas P. Rogan [mailto:sprogan@...]
                Sent: Friday, December 31, 2004 1:14 PM
                To: ai-geostats@...
                Subject: [ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW


                Hello everyone,

                I apologize if this question is too elementary for this list;
                I want to understand the key differences between linear regression,
                kriging, conditional simulation and other interpolation techniques such as
                IDW or splines in the analyses of spatial data. I would like to know the
                assumptions, strengths and weaknesses of each method, and when one method
                should be preferred to another. I browsed the archives and looked at some
                of the on-line papers, but they are written at a level beyond my own
                current understanding. It seems to me that this would be a great topic for
                the first chapter of an introductory spatial analysis textbook. Can anyone
                recommend any basic textbooks or references on this topic?
                Any assistance you can offer would be appreciated.

                Sincerely,

                Seumas Rogan
              • Volker Bahn
                Hi all, picking up on Jeff s point about collocated cokriging: what is the difference between this technique (which I m not familiar with) and an
                Message 7 of 16 , Jan 3, 2005
                  Hi all,

                  picking up on Jeff's point about collocated cokriging: what is the
                  difference between this technique (which I'm not familiar with) and an
                  autoregressive regression models such as CAR, SAR etc?

                  Thanks

                  Volker


                  _______________________________

                  Volker Bahn

                  Dept. of Wildlife Ecology - Rm. 210
                  University of Maine
                  5755 Nutting Hall
                  Orono, Maine
                  04469-5755, USA
                  Tel. (207) 581 2799
                  Fax: (207) 581 2858
                  volker.bahn@...
                  http://www.wle.umaine.edu/used_text%20files/Volker%20Bahn/home.htm-----
                  Original Message -----
                  From: "jyarus" <jyarus@...>
                  To: "'Seumas P. Rogan'" <sprogan@...>; <ai-geostats@...>
                  Sent: Monday, January 03, 2005 12:34
                  Subject: RE: [ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW


                  | Hi Seumas:
                  |
                  | I thought I would throw my 2 cents in regarding a comparison between
                  kriging
                  | and linear regression.
                  |
                  | While some of the responses have hit a few important differences, like
                  | Kriging is a spatial estimator and regression is not, or kriging will
                  honor
                  | the original data and regression will not (unless residuals are added back
                  | in - not often done). For me, the critical point to be made is between
                  the
                  | collocated cokriging application and regression. In collocated cokriging,
                  | like simple regression, two variables are being used, one independent and
                  | one dependent (of course, this could be expanded to more than one
                  | independent variable). The object is to predict a value of the dependent
                  | variable from a relationship established between both the independent and
                  | dependent observed values. In the ensuing regression equation, there is a
                  | slope term. For example, in the equation, Y= c-bX, c is the intercept and
                  b
                  | is the slope. As pointed out by one of the contributors, regression by
                  | itself is not a spatial estimator, it is a point estimator. As such, the
                  | equation contains no information about the surrounding data or about the
                  | relationship between the observed data and the unsampled location where a
                  | desired estimate of the dependent variable is required. In kriging (or
                  | cokriging), the slope term "b" is replaced by a covariance matrix that
                  | informs the system not only about the behavior of the surrounding data
                  | points and the unsampled location (similar to distance weighting if
                  | omnidirectional), but also about the spatial behavior within the
                  | neighborhood - that is, how neighbors are spatially related to other
                  | neighbors. Thus, the slope term "b" is replaced with a sophisticated
                  | covariance matrix containing the spatial information.
                  |
                  | The ramifications of using simple regression instead of true spatial
                  | estimator are significant if the results are presented in map form. While
                  | this is often difficult to grasp for some, using simple regression as a
                  | mapping tool will cause geographic portions of a map to consistently be
                  | overestimated and others underestimated! For example, you may find that
                  all
                  | the values estimated in the upper left quadrant of the map to be
                  | overestimated, and those in the lower right to be underestimated. We
                  would
                  | like to believe that a good spatial estimator will be unbiased, and the
                  | distribution of the error variances over the area of a map will be
                  uniform -
                  | no one part of the map will preferentially over- or underestimated. The
                  | bias brought about by the slope term in simple regression can be easily
                  | tested and proved.
                  |
                  | I have attached a short paper my partner Richard Chambers and I published
                  in
                  | the Canadian Recorder a few years back which addressed this issue. The
                  | article talks about seismic attributes related to petroleum reservoir
                  | characterization. However, beginning around page 10 or 11, we give an
                  | example that demonstrates the above points.
                  |
                  | I hope this is informative and useful.
                  |
                  | King Regards,
                  |
                  | Jeffrey M. Yarus
                  | ------------------------------------
                  | QGSI
                  | Jeffrey M. Yarus
                  | Partner
                  | jyarus@...
                  | 2900 Wilcrest, Suite 370
                  | Houston, Texas 77042
                  | tel: (713) 789-9331
                  | fax: (713) 789-9318
                  | mobile: (832) 630-7128
                  | ------------------------------------
                  |
                  | -----Original Message-----
                  | From: Seumas P. Rogan [mailto:sprogan@...]
                  | Sent: Friday, December 31, 2004 1:14 PM
                  | To: ai-geostats@...
                  | Subject: [ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW
                  |
                  |
                  | Hello everyone,
                  |
                  | I apologize if this question is too elementary for this list;
                  | I want to understand the key differences between linear regression,
                  | kriging, conditional simulation and other interpolation techniques such as
                  | IDW or splines in the analyses of spatial data. I would like to know the
                  | assumptions, strengths and weaknesses of each method, and when one method
                  | should be preferred to another. I browsed the archives and looked at some
                  | of the on-line papers, but they are written at a level beyond my own
                  | current understanding. It seems to me that this would be a great topic for
                  | the first chapter of an introductory spatial analysis textbook. Can anyone
                  | recommend any basic textbooks or references on this topic?
                  | Any assistance you can offer would be appreciated.
                  |
                  | Sincerely,
                  |
                  | Seumas Rogan
                  |
                  |
                  |
                  |


                  --------------------------------------------------------------------------------


                  |* By using the ai-geostats mailing list you agree to follow its rules
                  | ( see http://www.ai-geostats.org/help_ai-geostats.htm )
                  |
                  | * To unsubscribe to ai-geostats, send the following in the subject or in
                  the body (plain text format) of an email message to sympa@...
                  |
                  | Signoff ai-geostats
                • Syed Abdul Rahman Shibli
                  Perhaps there is some confusion here. Simple kriging, for instance, can be decomposed to the familiar multilinear regression equation since if one assumes all
                  Message 8 of 16 , Jan 4, 2005
                    Perhaps there is some confusion here. Simple kriging, for instance, can be
                    decomposed to the familiar multilinear regression equation since if one
                    assumes all the Z(Xi)s are independent variables, then in the covariance
                    matrix C all of C(Xi,Xj) would be zero except for C(Xi,Xi). So

                    LiC(Xi,Xi)=C(Xi,Xo)

                    The lambdas here being the parameters of the regression equation. The
                    intercept term is the sam, i.e. Lo=E(y)-LiE(xi).

                    Not sure if the previous poster meant this or simply using the location as
                    the "independent" variable.

                    Cheers

                    Syed

                    On 3/1/05 5:34 PM, "jyarus" <jyarus@...> wrote:

                    > Hi Seumas:
                    >
                    > I thought I would throw my 2 cents in regarding a comparison between kriging
                    > and linear regression.
                    >
                    > While some of the responses have hit a few important differences, like
                    > Kriging is a spatial estimator and regression is not, or kriging will honor
                    > the original data and regression will not (unless residuals are added back
                    > in - not often done). For me, the critical point to be made is between the
                    > collocated cokriging application and regression. In collocated cokriging,
                    > like simple regression, two variables are being used, one independent and
                    > one dependent (of course, this could be expanded to more than one
                    > independent variable). The object is to predict a value of the dependent
                    > variable from a relationship established between both the independent and
                    > dependent observed values. In the ensuing regression equation, there is a
                    > slope term. For example, in the equation, Y= c-bX, c is the intercept and b
                    > is the slope. As pointed out by one of the contributors, regression by
                    > itself is not a spatial estimator, it is a point estimator. As such, the
                    > equation contains no information about the surrounding data or about the
                    > relationship between the observed data and the unsampled location where a
                    > desired estimate of the dependent variable is required. In kriging (or
                    > cokriging), the slope term "b" is replaced by a covariance matrix that
                    > informs the system not only about the behavior of the surrounding data
                    > points and the unsampled location (similar to distance weighting if
                    > omnidirectional), but also about the spatial behavior within the
                    > neighborhood - that is, how neighbors are spatially related to other
                    > neighbors. Thus, the slope term "b" is replaced with a sophisticated
                    > covariance matrix containing the spatial information.
                    >
                    > The ramifications of using simple regression instead of true spatial
                    > estimator are significant if the results are presented in map form. While
                    > this is often difficult to grasp for some, using simple regression as a
                    > mapping tool will cause geographic portions of a map to consistently be
                    > overestimated and others underestimated! For example, you may find that all
                    > the values estimated in the upper left quadrant of the map to be
                    > overestimated, and those in the lower right to be underestimated. We would
                    > like to believe that a good spatial estimator will be unbiased, and the
                    > distribution of the error variances over the area of a map will be uniform -
                    > no one part of the map will preferentially over- or underestimated. The
                    > bias brought about by the slope term in simple regression can be easily
                    > tested and proved.
                    >
                    > I have attached a short paper my partner Richard Chambers and I published in
                    > the Canadian Recorder a few years back which addressed this issue. The
                    > article talks about seismic attributes related to petroleum reservoir
                    > characterization. However, beginning around page 10 or 11, we give an
                    > example that demonstrates the above points.
                    >
                    > I hope this is informative and useful.
                    >
                    > King Regards,
                    >
                    > Jeffrey M. Yarus
                    > ------------------------------------
                    > QGSI
                    > Jeffrey M. Yarus
                    > Partner
                    > jyarus@...
                    > 2900 Wilcrest, Suite 370
                    > Houston, Texas 77042
                    > tel: (713) 789-9331
                    > fax: (713) 789-9318
                    > mobile: (832) 630-7128
                    > ------------------------------------
                    >
                    > -----Original Message-----
                    > From: Seumas P. Rogan [mailto:sprogan@...]
                    > Sent: Friday, December 31, 2004 1:14 PM
                    > To: ai-geostats@...
                    > Subject: [ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW
                    >
                    >
                    > Hello everyone,
                    >
                    > I apologize if this question is too elementary for this list;
                    > I want to understand the key differences between linear regression,
                    > kriging, conditional simulation and other interpolation techniques such as
                    > IDW or splines in the analyses of spatial data. I would like to know the
                    > assumptions, strengths and weaknesses of each method, and when one method
                    > should be preferred to another. I browsed the archives and looked at some
                    > of the on-line papers, but they are written at a level beyond my own
                    > current understanding. It seems to me that this would be a great topic for
                    > the first chapter of an introductory spatial analysis textbook. Can anyone
                    > recommend any basic textbooks or references on this topic?
                    > Any assistance you can offer would be appreciated.
                    >
                    > Sincerely,
                    >
                    > Seumas Rogan
                    >
                    >
                    >
                    > * By using the ai-geostats mailing list you agree to follow its rules
                    > ( see http://www.ai-geostats.org/help_ai-geostats.htm )
                    >
                    > * To unsubscribe to ai-geostats, send the following in the subject or in the
                    > body (plain text format) of an email message to sympa@...
                    >
                    > Signoff ai-geostats
                  • Darla Munroe
                    Just to get the group s opinion on this - When do you use IDW? When is it an advantageous technique, or what purposes does it well serve? Darla Munroe ...
                    Message 9 of 16 , Jan 4, 2005
                      Just to get the group's opinion on this -

                      When do you use IDW? When is it an advantageous technique, or what purposes
                      does it well serve?

                      Darla Munroe

                      -----Original Message-----
                      From: Syed Abdul Rahman Shibli [mailto:sshibli@...]
                      Sent: Tuesday, January 04, 2005 2:19 PM
                      To: jyarus; 'Seumas P. Rogan'; ai-geostats@...
                      Subject: Re: [ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW


                      Perhaps there is some confusion here. Simple kriging, for instance, can be
                      decomposed to the familiar multilinear regression equation since if one
                      assumes all the Z(Xi)s are independent variables, then in the covariance
                      matrix C all of C(Xi,Xj) would be zero except for C(Xi,Xi). So

                      LiC(Xi,Xi)=C(Xi,Xo)

                      The lambdas here being the parameters of the regression equation. The
                      intercept term is the sam, i.e. Lo=E(y)-LiE(xi).

                      Not sure if the previous poster meant this or simply using the location as
                      the "independent" variable.

                      Cheers

                      Syed

                      On 3/1/05 5:34 PM, "jyarus" <jyarus@...> wrote:

                      > Hi Seumas:
                      >
                      > I thought I would throw my 2 cents in regarding a comparison between
                      kriging
                      > and linear regression.
                      >
                      > While some of the responses have hit a few important differences, like
                      > Kriging is a spatial estimator and regression is not, or kriging will
                      honor
                      > the original data and regression will not (unless residuals are added back
                      > in - not often done). For me, the critical point to be made is between
                      the
                      > collocated cokriging application and regression. In collocated cokriging,
                      > like simple regression, two variables are being used, one independent and
                      > one dependent (of course, this could be expanded to more than one
                      > independent variable). The object is to predict a value of the dependent
                      > variable from a relationship established between both the independent and
                      > dependent observed values. In the ensuing regression equation, there is a
                      > slope term. For example, in the equation, Y= c-bX, c is the intercept and
                      b
                      > is the slope. As pointed out by one of the contributors, regression by
                      > itself is not a spatial estimator, it is a point estimator. As such, the
                      > equation contains no information about the surrounding data or about the
                      > relationship between the observed data and the unsampled location where a
                      > desired estimate of the dependent variable is required. In kriging (or
                      > cokriging), the slope term "b" is replaced by a covariance matrix that
                      > informs the system not only about the behavior of the surrounding data
                      > points and the unsampled location (similar to distance weighting if
                      > omnidirectional), but also about the spatial behavior within the
                      > neighborhood - that is, how neighbors are spatially related to other
                      > neighbors. Thus, the slope term "b" is replaced with a sophisticated
                      > covariance matrix containing the spatial information.
                      >
                      > The ramifications of using simple regression instead of true spatial
                      > estimator are significant if the results are presented in map form. While
                      > this is often difficult to grasp for some, using simple regression as a
                      > mapping tool will cause geographic portions of a map to consistently be
                      > overestimated and others underestimated! For example, you may find that
                      all
                      > the values estimated in the upper left quadrant of the map to be
                      > overestimated, and those in the lower right to be underestimated. We
                      would
                      > like to believe that a good spatial estimator will be unbiased, and the
                      > distribution of the error variances over the area of a map will be uniform
                      -
                      > no one part of the map will preferentially over- or underestimated. The
                      > bias brought about by the slope term in simple regression can be easily
                      > tested and proved.
                      >
                      > I have attached a short paper my partner Richard Chambers and I published
                      in
                      > the Canadian Recorder a few years back which addressed this issue. The
                      > article talks about seismic attributes related to petroleum reservoir
                      > characterization. However, beginning around page 10 or 11, we give an
                      > example that demonstrates the above points.
                      >
                      > I hope this is informative and useful.
                      >
                      > King Regards,
                      >
                      > Jeffrey M. Yarus
                      > ------------------------------------
                      > QGSI
                      > Jeffrey M. Yarus
                      > Partner
                      > jyarus@...
                      > 2900 Wilcrest, Suite 370
                      > Houston, Texas 77042
                      > tel: (713) 789-9331
                      > fax: (713) 789-9318
                      > mobile: (832) 630-7128
                      > ------------------------------------
                      >
                      > -----Original Message-----
                      > From: Seumas P. Rogan [mailto:sprogan@...]
                      > Sent: Friday, December 31, 2004 1:14 PM
                      > To: ai-geostats@...
                      > Subject: [ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW
                      >
                      >
                      > Hello everyone,
                      >
                      > I apologize if this question is too elementary for this list;
                      > I want to understand the key differences between linear regression,
                      > kriging, conditional simulation and other interpolation techniques such as
                      > IDW or splines in the analyses of spatial data. I would like to know the
                      > assumptions, strengths and weaknesses of each method, and when one method
                      > should be preferred to another. I browsed the archives and looked at some
                      > of the on-line papers, but they are written at a level beyond my own
                      > current understanding. It seems to me that this would be a great topic for
                      > the first chapter of an introductory spatial analysis textbook. Can anyone
                      > recommend any basic textbooks or references on this topic?
                      > Any assistance you can offer would be appreciated.
                      >
                      > Sincerely,
                      >
                      > Seumas Rogan
                      >
                      >
                      >
                      > * By using the ai-geostats mailing list you agree to follow its rules
                      > ( see http://www.ai-geostats.org/help_ai-geostats.htm )
                      >
                      > * To unsubscribe to ai-geostats, send the following in the subject or in
                      the
                      > body (plain text format) of an email message to sympa@...
                      >
                      > Signoff ai-geostats
                    • Pierre Goovaerts
                      Well... I would say that IDW is still being used by a few consultants that think that kriging is too complicated to apply and that the client will pay them as
                      Message 10 of 16 , Jan 4, 2005
                        Well... I would say that IDW is still being used by a few consultants that
                        think that kriging is too complicated to apply and that the client will pay
                        them as long as the map looks pretty...
                        and less cynically IDW could give OK results if your data are gridded
                        and the pattern of variability is ostropic.

                        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: Darla Munroe [mailto:munroe.9@...]
                        Sent: Tue 1/4/2005 3:06 PM
                        To: ai-geostats@...
                        Cc:
                        Subject: RE: [ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW




                        Just to get the group's opinion on this -

                        When do you use IDW? When is it an advantageous technique, or what purposes
                        does it well serve?

                        Darla Munroe

                        -----Original Message-----
                        From: Syed Abdul Rahman Shibli [mailto:sshibli@...]
                        Sent: Tuesday, January 04, 2005 2:19 PM
                        To: jyarus; 'Seumas P. Rogan'; ai-geostats@...
                        Subject: Re: [ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW


                        Perhaps there is some confusion here. Simple kriging, for instance, can be
                        decomposed to the familiar multilinear regression equation since if one
                        assumes all the Z(Xi)s are independent variables, then in the covariance
                        matrix C all of C(Xi,Xj) would be zero except for C(Xi,Xi). So

                        LiC(Xi,Xi)=C(Xi,Xo)

                        The lambdas here being the parameters of the regression equation. The
                        intercept term is the sam, i.e. Lo=E(y)-LiE(xi).

                        Not sure if the previous poster meant this or simply using the location as
                        the "independent" variable.

                        Cheers

                        Syed

                        On 3/1/05 5:34 PM, "jyarus" <jyarus@...> wrote:

                        > Hi Seumas:
                        >
                        > I thought I would throw my 2 cents in regarding a comparison between
                        kriging
                        > and linear regression.
                        >
                        > While some of the responses have hit a few important differences, like
                        > Kriging is a spatial estimator and regression is not, or kriging will
                        honor
                        > the original data and regression will not (unless residuals are added back
                        > in - not often done). For me, the critical point to be made is between
                        the
                        > collocated cokriging application and regression. In collocated cokriging,
                        > like simple regression, two variables are being used, one independent and
                        > one dependent (of course, this could be expanded to more than one
                        > independent variable). The object is to predict a value of the dependent
                        > variable from a relationship established between both the independent and
                        > dependent observed values. In the ensuing regression equation, there is a
                        > slope term. For example, in the equation, Y= c-bX, c is the intercept and
                        b
                        > is the slope. As pointed out by one of the contributors, regression by
                        > itself is not a spatial estimator, it is a point estimator. As such, the
                        > equation contains no information about the surrounding data or about the
                        > relationship between the observed data and the unsampled location where a
                        > desired estimate of the dependent variable is required. In kriging (or
                        > cokriging), the slope term "b" is replaced by a covariance matrix that
                        > informs the system not only about the behavior of the surrounding data
                        > points and the unsampled location (similar to distance weighting if
                        > omnidirectional), but also about the spatial behavior within the
                        > neighborhood - that is, how neighbors are spatially related to other
                        > neighbors. Thus, the slope term "b" is replaced with a sophisticated
                        > covariance matrix containing the spatial information.
                        >
                        > The ramifications of using simple regression instead of true spatial
                        > estimator are significant if the results are presented in map form. While
                        > this is often difficult to grasp for some, using simple regression as a
                        > mapping tool will cause geographic portions of a map to consistently be
                        > overestimated and others underestimated! For example, you may find that
                        all
                        > the values estimated in the upper left quadrant of the map to be
                        > overestimated, and those in the lower right to be underestimated. We
                        would
                        > like to believe that a good spatial estimator will be unbiased, and the
                        > distribution of the error variances over the area of a map will be uniform
                        -
                        > no one part of the map will preferentially over- or underestimated. The
                        > bias brought about by the slope term in simple regression can be easily
                        > tested and proved.
                        >
                        > I have attached a short paper my partner Richard Chambers and I published
                        in
                        > the Canadian Recorder a few years back which addressed this issue. The
                        > article talks about seismic attributes related to petroleum reservoir
                        > characterization. However, beginning around page 10 or 11, we give an
                        > example that demonstrates the above points.
                        >
                        > I hope this is informative and useful.
                        >
                        > King Regards,
                        >
                        > Jeffrey M. Yarus
                        > ------------------------------------
                        > QGSI
                        > Jeffrey M. Yarus
                        > Partner
                        > jyarus@...
                        > 2900 Wilcrest, Suite 370
                        > Houston, Texas 77042
                        > tel: (713) 789-9331
                        > fax: (713) 789-9318
                        > mobile: (832) 630-7128
                        > ------------------------------------
                        >
                        > -----Original Message-----
                        > From: Seumas P. Rogan [mailto:sprogan@...]
                        > Sent: Friday, December 31, 2004 1:14 PM
                        > To: ai-geostats@...
                        > Subject: [ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW
                        >
                        >
                        > Hello everyone,
                        >
                        > I apologize if this question is too elementary for this list;
                        > I want to understand the key differences between linear regression,
                        > kriging, conditional simulation and other interpolation techniques such as
                        > IDW or splines in the analyses of spatial data. I would like to know the
                        > assumptions, strengths and weaknesses of each method, and when one method
                        > should be preferred to another. I browsed the archives and looked at some
                        > of the on-line papers, but they are written at a level beyond my own
                        > current understanding. It seems to me that this would be a great topic for
                        > the first chapter of an introductory spatial analysis textbook. Can anyone
                        > recommend any basic textbooks or references on this topic?
                        > Any assistance you can offer would be appreciated.
                        >
                        > Sincerely,
                        >
                        > Seumas Rogan
                        >
                        >
                        >
                        > * By using the ai-geostats mailing list you agree to follow its rules
                        > ( see http://www.ai-geostats.org/help_ai-geostats.htm )
                        >
                        > * To unsubscribe to ai-geostats, send the following in the subject or in
                        the
                        > body (plain text format) of an email message to sympa@...
                        >
                        > Signoff ai-geostats
                      • Edzer J. Pebesma
                        ... I use IDW to plot a smooth surface, fitted through the data points. This may serve as another spatial visualisation of the data; I see it as an exploratory
                        Message 11 of 16 , Jan 4, 2005
                          Darla Munroe wrote:
                          > Just to get the group's opinion on this -
                          >
                          > When do you use IDW? When is it an advantageous technique, or what purposes
                          > does it well serve?

                          I use IDW to plot a smooth surface, fitted through the data points.
                          This may serve as another spatial visualisation of the data; I see
                          it as an exploratory step towards building a statistical model for
                          spatial variation.
                          --
                          Edzer
                        • Isobel Clark
                          Syed The term independent variables is confusing in the context of regression. It does not mean that the variables are independent of one another. It means
                          Message 12 of 16 , Jan 4, 2005
                            Syed

                            The term "independent variables" is confusing in the
                            context of regression. It does not mean that the
                            variables are independent of one another. It means
                            that they are independent of the error incurred in the
                            estimation. The variance-covariance matrix is
                            classically produced directly from the data and does
                            not need to be diagonal.

                            The difference between simple kriging and regression
                            is solely that the covariances are derived from a
                            model rather than directly from the data.

                            Isobel
                            http://geoecosse.bizland.com/books.htm
                          • Isobel Clark
                            Agrred, IDW is a good rough way to visualise your data before embarking on more objective (?) approaches. If your data is pretty regularly spread out, small
                            Message 13 of 16 , Jan 4, 2005
                              Agrred, IDW is a good rough way to visualise your data
                              before embarking on more 'objective'(?) approaches.

                              If your data is pretty regularly spread out, small
                              nugget effect and you use the semi-variogram to choose
                              the search radii, there is little difference between
                              an IDW-squared map and kriging.

                              Isobel
                            • Digby Millikan
                              Seumas, I was probably a bit misleading to say regression is not an estimation technique. The word regression meaning to revert back to the original, or find
                              Message 14 of 16 , Jan 5, 2005
                                Seumas,

                                I was probably a bit misleading to say regression
                                is not an estimation technique. The word regression
                                meaning to revert back to the original, or find the
                                underlying real equation for a set of data. "Kriging"
                                is a form of what is called "generalised linear regression"
                                which is one of the most advanced forms of regression.
                                The simpler forms of regression can be used to fit
                                parametrics equations to data, such as linear regression
                                to fit an equation of a line to a set of data points,
                                or non-linear regression to fit a polynomial surface
                                to a scattered set of say topography data points.
                                Not really estimation, but equation fitting. I use non-linear
                                regression to fit equations to drillhole survey points
                                to plot their curves. In it's more advanced form when
                                you wish to fit equations to say a set of two dimensional
                                data points, or three dimensional orebody samples,
                                this is called trend surface fitting. Unfortunately normally
                                the equations developed from trend surface fitting
                                become massively too complex to handle to be practical,
                                and hence estimation is opted for.

                                Digby
                              • Digby Millikan
                                For ore resource modelling I ve used IDW on a highly skewed lognormally distributed deposit, where no variograms could be produced. With lognormally
                                Message 15 of 16 , Jan 5, 2005
                                  For ore resource modelling I've used IDW on a highly skewed lognormally
                                  distributed deposit, where no variograms could be produced. With lognormally
                                  distributed data often found in ore resources, having a good variogram is
                                  important, to avoid large errors in kriging hence it may be preferential to
                                  use
                                  IDW and a topcut. However if your data is not so highly skewed even
                                  approximating
                                  a variogram can provide superior results. I used to model topography
                                  surfaces
                                  and Kriging with a 'guessed' variogram produced good results compared to
                                  IDW which produced highly spiked and erroneous results.

                                  Digby
                                  www.users.on.net/~digbym
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