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RE: AI-GEOSTATS: mysterious kriging output

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  • richardh@hellscho.com.au
    Noemi I am not too sure what you mean by mysterious kriging output - your attached plans appear okay to me, the model appears to reflect the underlying data
    Message 1 of 2 , Mar 8 8:59 PM
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      Noemi

      I am not too sure what you mean by "mysterious kriging output" - your
      attached plans appear okay to me, the model appears to reflect the
      underlying data reasonably well. The "plaid effect" that you refer to -
      seen on the variance map makes sense. There seems to be a general
      mis-conception that kriging variance is related to the actual data values -
      this is not the case. Kriging variance is related, pure and simply, to data
      configuration - in areas where there is a lot of data the kriging variance
      is low, where there is little data the variance is high.

      Hope this helps.

      Richard Hague



      Original Message:
      -----------------
      From: Noemi Barabas barabas@...
      Date: Mon, 8 Mar 2004 18:18:55 -0500 (EST)
      To: ai-geostats@...
      Subject: AI-GEOSTATS: mysterious kriging output


      Dear list,

      I am working on a kriging problem of log-PCB concentrations in
      river sediments (the coordinates have been "straightened"), using GSLib.
      I have strong anisotropy with a ratio of about 1:6 (x:y). I have some
      clustered locations as well as some sparsely sampled areas, and several
      instances where the high and low concentrations are found very close to
      eachother. The distribution is lognormal and I am working with
      log-transformed values. The variograms are rather nice in both
      directions. Nevertheless, ordinary kriging gives a very peculiar-looking
      map (of log-concentrations). It would be too difficult to put into
      words, so I have included maps of estimates, variance and local mean as
      an attachment.

      Does anybody know what causes this "plaid" effect? Looking at the map
      of variances, it appears that an estimation location has low variance
      if it has a data point directly above and next to it, but intermediate
      variance if those same two data points are in a diagonal direction
      relative to the axes of anisotropy, even if the new position takes the
      estimation point closer to the data points. I would like to undestand the
      reason for this effect, as well as whether there is something that can be
      done about it.

      Could the fact that there are high values embedded in low value locations
      be partially responsible for these strange maps?

      (I did experiment with octant search, various maximum search radii,
      various min and max number of data points for estimation, and this effect
      persists. I even reversed the angles of anisotropy, tried different
      variogram ranges. The variogram ranges are about 20% of the width/length
      of the domain, and the relative nugget effect is about 6% in both
      directions)

      Thanks very much!

      Noemi




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    • Monica Palaseanu-Lovejoy
      Hi Ruben, thanks so much for the references .... and especially the R routines .... i will look into it. This may really give some good answers to my data -
      Message 2 of 2 , Mar 9 4:29 AM
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        Hi Ruben,

        thanks so much for the references .... and especially the R
        routines .... i will look into it. This may really give some good
        answers to my data - once for all - i hope at least. I think we
        neglect in majority of cases to verify if the data come from one or 2
        (or more) distributions and just apply a transformation and do a
        kriging .... it is just too easy that way ;-))

        Again, thank you so much,

        Monica

        > Exploratory analysis of the frequency distribution of the data (i.e. the
        > aggregated, non-spatial, frequency) could reveal the existence of two (or
        > more) populations. To evaluate the evidence in favour of such an
        > hypothesis, you could compare the hypothesis that the frequency
        > distribution is formed by a mixture of two (or more) specified
        > distributions versus the hypothesis that it is formed by only one. The
        > general topic in statistics is called 'mixture distribution analysis' (not
        > to be confused with 'mixture models'). Useful references are:
        >
        > Everitt & Hand, 1981, Mixture distribution analysis. Chapman & Hall
        > Chen & Chen, 2001, Statistics and Probability Letters 52:125
        > Hawkins et al., 2001, Computational Statistics & Data Analysis 38:15
        > http://www.math.mcmaster.ca/peter/mix/mix.html
        >
        > Some robust regression methods, for example, are based on treating the
        > data as coming from a mixture of two distributions, the main one, and a
        > contaminating distribution.
        >
        > If you conclude that there are two (or more) distributions, then you can
        > compute the maximum conditional probability that any given data point
        > belong to any of the two (or more) distributions, and use this computation
        > to classify data. After this exploratory analysis, you could treat the two
        > (or more) populations differently, if there is evidence for a mixture, and
        > maybe even perform separate geostatistical analyses on the separate
        > populations.
        >
        > I used this general strategy in the analysis of a time series of an index
        > of returns from investments in finantial markets. The strategy was
        > proposed by Hamilton, 1994, Time Series Analysis, Ch. 22, Princeton U. P.
        >
        > Ruben



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