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P.S. Re: [ai-geostats] Regression vs. Kriging vs. Simulation vs. IDW

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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 1 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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    • 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 2 of 16 , Jan 4, 2005
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        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 3 of 16 , Jan 4, 2005
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          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 4 of 16 , Jan 4, 2005
          • 0 Attachment
            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 5 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 6 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 7 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 8 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 9 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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