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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
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      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
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        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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      • 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 3 of 16 , Jan 3, 2005
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          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 4 of 16 , Jan 3, 2005
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            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 5 of 16 , Jan 3, 2005
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              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 6 of 16 , Jan 4, 2005
              • 0 Attachment
                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 7 of 16 , Jan 4, 2005
                • 0 Attachment
                  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 )
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                • 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 8 of 16 , Jan 4, 2005
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                    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 9 of 16 , Jan 4, 2005
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                      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 10 of 16 , Jan 4, 2005
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                        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 11 of 16 , Jan 4, 2005
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                          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 12 of 16 , Jan 5, 2005
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                            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 13 of 16 , Jan 5, 2005
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                              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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