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AI-GEOSTATS: SUM: estimating mean of irregular block

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  • William Thayer
    I would like to thank (in the order in which I received their responses) Pierre Goovaerts, Isobel Clark and Edzer Pebesma for their assistance. The original
    Message 1 of 5 , Mar 29, 2001
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      I would like to thank (in the order in which I received their responses)
      Pierre Goovaerts, Isobel Clark and Edzer Pebesma for their assistance.
      The original post appears at the end of the message.

      Pierre sent a copy of one of his publications that addresses the estimation
      of the block means (Goovaerts, P. 1999. Geostatistical tools for deriving
      block-averaged values of environmental attributes. Journal of Geographical
      Information Sciences, 5(2), 88-96.)

      Isobel suggested the demo version of the PG2000 software or (also free) new
      kriging game. Both of which are available at
      http://uk.geocities.com/drisobelclark
      Isobel also referred me to one of her papers: "Practical kriging in three
      dimensions", Computers and Geosciences, Vol 3, pp.173--180. I have chosen
      to order her new book, which also covers the subject.

      Edzer offered to run Gstat using my data and parameter files. As he
      indicated in a separate post earlier today, the problem was not with Gstat
      but with the user(!): I was not defining the neighborhood search as I
      intended. This brought up another issue: given the algorithm that is
      typically used to estimate the mean of a block, the size of a block one can
      krig is limited by the range of the variogram (provided one is interested
      in obtaining an estimate of the variance of the mean). This seems to
      indicate another advantage of simulation methods.


      Original Post:

      I am looking for references that address estimating the mean of an
      irregular block using kriging.

      I want to estimate the mean concentration within a polygon in which a
      limited number of observations are located. I wish to supplement the
      limited number of observations with observations that are found outside of
      the polygon (but nearby). My goal is to reduce the uncertainty in the
      mean concentration by using additional observations. I have recently
      started using Gstat to perform this type of calculation.

      My questions are: 1) What does the kriging variance for the irregular block
      represent and how can it be used to construct confidence intervals? In
      some cases, the kriging variance appears to be unreasonably high. 2)
      During some testing of Gstat, I have noticed that when I increase the area
      of the irregular block beyond approximately one half of the site, Gstat
      produces an estimate that is approximately three times the mean of the
      observations located within the area. Has anyone encountered this with
      Gstat before?
      **************************************************
      William C. Thayer, P.E.

      Environmental Science Center
      Syracuse Research Corporation
      6225 Running Ridge Road
      North Syracuse, NY 13212-2510
      phone: (315) 452-8424
      fax: (315) 452-8090
      email: thayer@...
      **************************************************



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    • Edzer J. Pebesma
      ... Why? Why can t you for instance block-krige the mean for the entire study area, provided that you use a suitable point discretisation for it? -- Edzer -- *
      Message 2 of 5 , Mar 29, 2001
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        William Thayer wrote:

        > This brought up another issue: given the algorithm that is
        > typically used to estimate the mean of a block, the size of a block one can
        > krig is limited by the range of the variogram (provided one is interested
        > in obtaining an estimate of the variance of the mean). This seems to
        > indicate another advantage of simulation methods.

        Why? Why can't you for instance block-krige the mean for the entire study area,
        provided that you use a suitable point discretisation for it?
        --
        Edzer

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      • Isobel Clark
        ... I never heard that the size of the block restricted the estimation by the range of influence. Of course, all the algorithms I use search outside the block
        Message 3 of 5 , Mar 30, 2001
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          > Why? Why can't you for instance block-krige the mean
          > for the entire study area,
          > provided that you use a suitable point
          > discretisation for it?
          > --
          > Edzer

          I never heard that the size of the block restricted
          the estimation by the range of influence. Of course,
          all the algorithms I use search outside the block from
          the edges outwards (regular or irregular).

          Block kriging the entire deposit gets a bit tricky if
          you have a lot of samples, because the computation of
          the equations gets wobbly. Better to krige a few large
          blocks and combine them.

          Isobel Clark

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        • Edzer J. Pebesma
          ... With how many samples do things, as you say, get wobbly? How exactly would you combine block kriging variances? -- Edzer -- * To post a message to the
          Message 4 of 5 , Mar 30, 2001
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            Isobel Clark wrote:

            > Block kriging the entire deposit gets a bit tricky if
            > you have a lot of samples, because the computation of
            > the equations gets wobbly. Better to krige a few large
            > blocks and combine them.

            With how many samples do things, as you say, get wobbly?
            How exactly would you combine block kriging variances?
            --
            Edzer

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          • Isobel Clark
            ... That depends on (a) the software algorithms and (b) the computer you are using. Even with caution, you probably don t want to be solving equations with
            Message 5 of 5 , Mar 30, 2001
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              > With how many samples do things, as you say, get
              > wobbly?
              That depends on (a) the software algorithms and (b)
              the computer you are using. Even with caution, you
              probably don't want to be solving equations with more
              than 80-100 samples on a PC.

              There are people who know a lot more about this than
              I. Our own software is limited to 80 equations for one
              estimation.

              > How exactly would you combine block kriging
              > variances?
              If your blocks are big enough (or far enough apart) to
              be considered 'independent' of one another, then you
              can combine variances as per classical statistics
              using the square of the area/volume/tonnage as
              weighting.

              How big is big? How long is a piece of string?
              Isobel

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