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AI-GEOSTATS: log-normal kriging error

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  • Marta Rufino
    Dear list members, I have been calculating log-normal kriging for a data set using geoR.... and I obtained suspicious estimations... so I tried with another
    Message 1 of 6 , Dec 2, 2003
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      Dear list members,


      I have been calculating log-normal kriging for a data set using geoR....
      and I obtained suspicious estimations... so I tried with another data set,
      and I got the same...
      I am wondering that maybe there is another problem.... like the data not
      being strictly log-normal.. could this give such a huge variances?

      Sample data is (min, mean and max):
      0 23 314
      std. error: 59.55

      If I do OK, I get:
      predictions:
      -6 31 218
      std err.:
      27 40 55

      If I do log-OK I get:
      predictions:
      0.52 37 333
      std. err.:
      2 140 584

      Any ideia why I get such a huge variances when using log-normal kriging?
      Is it a problem of the data distribution? Is there any possibility of a
      code bug???

      Any comment will be muuuuch apreciated!

      Thank you
      Marta







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    • Isobel Clark
      Marta I am not familiar with the software you are using, but it looks like your lognormal standard errors are being back-transformed into raw units. If this
      Message 2 of 6 , Dec 3, 2003
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        Marta

        I am not familiar with the software you are using, but
        it looks like your lognormal standard errors are being
        back-transformed into 'raw' units. If this is the case
        part of the backtransform is to multiply the 'relative
        standard error' by the actual value of the estimate.

        That is, if your estimate is 0.52, the backtransformed
        standard error is multiplied by 0.52. If the estimate
        is 520, it is multiplied by 520. If you do a ratio
        between the standard error and the estimate, you will
        probably get equivalent 'relative' errors.

        We find it better to leave the standard errors in
        logarithms and use Sichel type confidence interval,
        using the lognormal model.

        Isobel
        http://uk.geocities.com/drisobelclark

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      • Gali Sirkis
        Dear list members, Please advise what to do in following case: The sparse dataset for kriging inlcudes only few (5-6) original data points + interpolated
        Message 3 of 6 , Dec 3, 2003
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          Dear list members,

          Please advise what to do in following case:
          The sparse dataset for kriging inlcudes only few
          (5-6) original data points + interpolated external
          data, that covering whole study area.
          One of the original data points seems completly not to
          fit to the main correlation line between original and
          external data, however mostly probable is not an
          error, but might represent different combination of
          data properties.
          Is there is any chance to use this outlying point?
          Does is sound feasible for you as specialists in
          statistical analysis to use the kriging method in this
          case?

          Many thanks in advance for your help,

          Gali Sirkis

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        • Monica Palaseanu-Lovejoy
          Hi, I am not sure i understood correctly your question. Fist of all, do the interpolated data have come from your sparse data interpolation? What method of
          Message 4 of 6 , Dec 3, 2003
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            Hi,

            I am not sure i understood correctly your question. Fist of all, do
            the interpolated data have come from your sparse data
            interpolation? What method of interpolation did you use in this
            case?

            After Burrough and McDonnel, 2000, you need at least 50 points to
            have reliable results through kriging. Certainly you can do it on less
            data, but until now i never saw a study considering this problem in
            depth (maybe there is literature out there, and if it does and
            anybody knows about it - i would like to know it also ;-))

            Secondly, if you know the outlier is not an error, but you interpret it
            as representing a different combination of properties than the rest
            of your data - i am not very sure it is wise to use it together with
            your rest of the data in any interpolation exercise. The outlier may
            represent a different population and in this case i cannot see any
            "physical" reason to treat all your data together if parts of the data
            represent different things. At least this is my opinion.

            Besides, if your data is not only sparse (5 or 6 data points .... it is
            really very sparse i think) but also far away in space, they can be
            at distances grater than the spatial correlation range, and in this
            case i really don't think you can use kriging .... you will have either
            a pure nugget effect or a very high nugget value and not a too high
            spatial correlation.

            Monica

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          • Gali Sirkis
            Hi Monica, thanks for quick reply. The interpolated data is a different data set with is by its nature (speaking about geological properties) should be
            Message 5 of 6 , Dec 3, 2003
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              Hi Monica,

              thanks for quick reply. The interpolated data is a
              different data set with is by its nature (speaking
              about geological properties) should be correlated with
              the sparse one.
              This is a geological data over not huge area - around
              20x30 kilometers. It should have at least some spatial
              correlation. The variogram is not of striking beauty
              :) but it is not a pure nugget effect, though.
              The only other way meaningfully interpolate between
              those sparse points, it seems to use the simple linear
              regression between those two datasets.
              The literature about kriging/interpolating for very
              sparse data would definitely help, if anybody know
              about, please let know.

              Thanks,

              Gali


              --- Monica Palaseanu-Lovejoy
              <monica.palaseanu-lovejoy@...> wrote:
              > Hi,
              >
              > I am not sure i understood correctly your question.
              > Fist of all, do
              > the interpolated data have come from your sparse
              > data
              > interpolation? What method of interpolation did you
              > use in this
              > case?
              >
              > After Burrough and McDonnel, 2000, you need at least
              > 50 points to
              > have reliable results through kriging. Certainly you
              > can do it on less
              > data, but until now i never saw a study considering
              > this problem in
              > depth (maybe there is literature out there, and if
              > it does and
              > anybody knows about it - i would like to know it
              > also ;-))
              >
              > Secondly, if you know the outlier is not an error,
              > but you interpret it
              > as representing a different combination of
              > properties than the rest
              > of your data - i am not very sure it is wise to use
              > it together with
              > your rest of the data in any interpolation exercise.
              > The outlier may
              > represent a different population and in this case i
              > cannot see any
              > "physical" reason to treat all your data together if
              > parts of the data
              > represent different things. At least this is my
              > opinion.
              >
              > Besides, if your data is not only sparse (5 or 6
              > data points .... it is
              > really very sparse i think) but also far away in
              > space, they can be
              > at distances grater than the spatial correlation
              > range, and in this
              > case i really don't think you can use kriging ....
              > you will have either
              > a pure nugget effect or a very high nugget value and
              > not a too high
              > spatial correlation.
              >
              > Monica


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            • Marcel Vallée
              Gail Sorry for not responding earlier to your request. Your explanatory comment to Monica does not convince me as a exploration and mining geologist. I think
              Message 6 of 6 , Dec 5, 2003
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                Gail

                Sorry for not responding earlier to your request.

                Your explanatory comment to Monica does not convince me
                as a exploration and mining geologist. I think her comments are
                wise and should be considered.

                A 20x30 km area is a large one even when dealing with very
                uniform geology. Even in such conditions, different properties
                may be encountered, either as faults, vein or fracturation
                system, small intrusive bodies, mineral showings or deposits,
                pollution zones, etc.

                Such a small sample set as you have ["few (5-6) original data
                points + interpolated external data"] that covering whole study
                area] does not allow you to really appraise the validity and/or
                the geological cause of this "outlier." (There might be a
                sampling or assaying cause also). In such a case, it should be
                shown as an anomaly, not averaged out or kriged out.

                Excluding sampling/analytical problems, the outlier only has a
                "detection"value, meaning that the geology is not as uniform as
                expected and that additional geological observations and sampling
                in the vicinity is required to elucidate this problem.

                We should view geostatistics as an ancillary tool to understand a
                two or three dimensional "geological universe." Whenever data ara
                as sparse as in your exemple, kriged values should not replace
                and/or eliminate the potential meaning of sparse field observations.

                Sincerely


                Marcel Vallée

                ========================

                Marcel Vallée Eng., Geo.
                Géoconseil Marcel Vallée Inc.
                706 Routhier St
                Québec, Québec,
                Canada G1X 3J9
                Tel: (1) 418, 652, 3497
                Email: vallee.marcel@...





                =========================================
                Gali Sirkis wrote:
                > Hi Monica,
                >
                > thanks for quick reply. The interpolated data is a
                > different data set with is by its nature (speaking
                > about geological properties) should be correlated with
                > the sparse one.
                > This is a geological data over not huge area - around
                > 20x30 kilometers. It should have at least some spatial
                > correlation. The variogram is not of striking beauty
                > :) but it is not a pure nugget effect, though.
                > The only other way meaningfully interpolate between
                > those sparse points, it seems to use the simple linear
                > regression between those two datasets.
                > The literature about kriging/interpolating for very
                > sparse data would definitely help, if anybody know
                > about, please let know.
                >
                > Thanks,
                >
                > Gali
                >
                >
                > --- Monica Palaseanu-Lovejoy
                > <monica.palaseanu-lovejoy@...> wrote:
                >
                >>Hi,
                >>
                >>I am not sure i understood correctly your question.
                >>Fist of all, do
                >>the interpolated data have come from your sparse
                >>data
                >>interpolation? What method of interpolation did you
                >>use in this
                >>case?
                >>
                >>After Burrough and McDonnel, 2000, you need at least
                >>50 points to
                >>have reliable results through kriging. Certainly you
                >>can do it on less
                >>data, but until now i never saw a study considering
                >>this problem in
                >>depth (maybe there is literature out there, and if
                >>it does and
                >>anybody knows about it - i would like to know it
                >>also ;-))
                >>
                >>Secondly, if you know the outlier is not an error,
                >>but you interpret it
                >>as representing a different combination of
                >>properties than the rest
                >>of your data - i am not very sure it is wise to use
                >>it together with
                >>your rest of the data in any interpolation exercise.
                >>The outlier may
                >>represent a different population and in this case i
                >>cannot see any
                >>"physical" reason to treat all your data together if
                >>parts of the data
                >>represent different things. At least this is my
                >>opinion.
                >>
                >>Besides, if your data is not only sparse (5 or 6
                >>data points .... it is
                >>really very sparse i think) but also far away in
                >>space, they can be
                >>at distances grater than the spatial correlation
                >>range, and in this
                >>case i really don't think you can use kriging ....
                >>you will have either
                >>a pure nugget effect or a very high nugget value and
                >>not a too high
                >>spatial correlation.
                >>
                >>Monica

                Dear list members,

                Please advise what to do in following case:
                The sparse dataset for kriging inlcudes only few
                (5-6) original data points + interpolated external
                data, that covering whole study area. One of the original data
                points seems completly not to
                fit to the main correlation line between original and
                external data, however mostly probable is not an
                error, but might represent different combination of
                data properties. Is there is any chance to use this outlying point?
                Does is sound feasible for you as specialists in
                statistical analysis to use the kriging method in this
                case?

                Many thanks in advance for your help,

                Gali Sirkis
                >
                >
                >
                > __________________________________
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                > Free Pop-Up Blocker - Get it now
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                >



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