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  • srahman@lgc.com
    ... some ... as ... Stationarity is a property of the random function model, and not necesarily a quality inherent in the actual data. The assumption can
    Message 1 of 3 , May 28, 1998
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      Andrew Lister wrote:
      >1. stationarity of the data: I have read a number of articles in the
      >ecology and agronomy literature discussing this concept, and have read
      some
      >conflicting things (one researcher refers to the concept of stationarity
      as
      >"troubling").
      Stationarity is a property of the random function model, and not necesarily
      a quality inherent in the actual data. The assumption can neither be proven
      nor refuted. However, this does not mean that it is a trivial decision --
      the
      way one pools the data would have an impact on decisions made
      later on in the kriging process, and could mean the difference between a
      map that makes sense and a pretty - though useless - picture. Knowledge
      of the underlying data (deterministic processes, experience, etc) can guide
      any decision to pool data together, and even give clues to potential
      inconsistencies, but an assumption remains an assumption.

      >2. checking for stationarity: I just finished reading a paper by Hamlett,
      >Horton and Cressie which shows some exploratory techniques for variogram
      >analysis. ... Obviously, this is not literal, but nobody
      >seems to say just how much change is ok for your data to be stationary,
      and
      >likewise with the variance.

      See previous comment on assuming stationarity. Even Cressie's example
      somewhere in his textbook applies two techniques to the same data, i.e.
      use of a power law model and after that median polish to filter out the
      trend. A cross validation exercise should give some idea of the more
      appropriate model to adopt.
      >3. trend removal: It's tempting just to say my data are non stationary
      and
      >do median polish and do my variograms with the residuals. Is this a
      valid,
      >albeit "black box", approach?

      There are two schools of thought here. The problem is inherent in the
      way residual variograms are calculated (biasedness) and used to
      make predictions. Some people can't live with the bias and use
      IRF-k techniques (intrinsic random functions of order k). Some just
      derive a trend surface, derive the residuals, calculate the variogram,
      perform a simple kriging, and then add the result back to the trend
      surface. The difference here IMHO is whether you want to use a
      true soup spoon or a normal spoon to eat your French onion
      soup. Both can probably get the job done, but you'd probably feel
      better doing the right thing by using a soup spoon.

      Refer Cressie's text with some results comparing generalized covariances
      visually (calculated using IRF-k) with the actual raw covariances. There
      seem to be less than a perfect fit. Any automatic fitting is a tricky
      process.
      >4. Could I simply fit a first or second order trend surface to the data,
      model
      >the variogram with my residuals, krig using ordinary kriging, and then add
      >the trend back in at the end as is suggested in the "final thoughts" of
      >Isaaks and Srivastava's book and elswhere (unless I am misinterpreting
      what
      >I read)?
      Rule of thumb is to use the highest order until you've removed the
      drift component, but IMHO and practically speaking second order is about
      as high as anyone would need.

      Regards,

      Syed


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    • Steve Zoraster
      ... I suggest that you look at the Approximate Nearest Neighbors (ANN) algorithm available at http://www/cs.umd/edu/~mount/ANN. ANN is a test bed for doing
      Message 2 of 3 , Sep 30, 1998
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        > > Bharat Lohani wrote:

        > > Please could you help me with....
        > >

        > > 2. I need to carry out some neighborhood operations with the
        > > data which is not in grid. This requires searching the
        > > full data set (approx. 1 M points ) evertime to find the
        > > points in the neighborhood of known locations. <snip>

        I suggest that you look at the Approximate Nearest Neighbors (ANN)
        algorithm available at http://www/cs.umd/edu/~mount/ANN. ANN is
        a "test bed" for doing approximate and _exact_ nearest neighbor
        (or k nearest neighbor) searches in multidimensional space....
        I haven't used it, but it looks interesting.

        Also consider "A Simple Algorithm for Nearest Neighbor Search in
        High Dimensions" by Nene and Nayar in IEEE Trans PAMA, Vol 19, No 9,
        Sept 97. I have read this article through, and the algorithm looks
        to me like the correct solution for 2D problems. I plan to use it
        in applications. A C++ implementation is available upon request
        from the authors (?) {sameer,nayar}@....


        > >
        > > Thanks in advance.
        > >
        > > Bharat.
        > > --

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      • srahman@lgc.com
        Not being familiar with landmines, other than the fact that they can maim or kill, I would wish that a bit more detail had been provided, since a majority of
        Message 3 of 3 , Feb 3, 2000
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          Not being familiar with landmines, other than the fact that
          they can maim or kill, I would wish that a bit more detail had
          been provided, since a majority of the readers can come from
          fields as diverse and arcane as pig husbandry and the
          population control of fruit bats. To wit:

          i. What is being mapped, and what is the potential impact of
          such maps on, e.g. human lives, if any?

          ii. What is a contaminant? How different is this from a plain
          vanilla landmine? Or are they one and the same thing?

          Are you trying to map the probabilities that a certain "contaminant"
          can exceed a certain level at discrete points in your region of
          interest? Perhaps a non-parametric method (indicator kriging) could
          be of use. Or are you trying to predict the probability that a landmine
          exists at a particular location (a binary on/off variable)? It is mentioned
          that the populations studied can be 1000 m2 or 1 million m2. Are these
          volumes of measurements? Areal expanse? What is a sample size
          of nearly "100%"?

          Syed









          Wilkinson Ms E <E.Wilkinson@...> on 02/04/2000 12:28:43 AM








          To: "'ai-geostats@...'"
          <ai-geostats@...>

          cc: (bcc: Syed Abdul Rahman/SINGPROD1/Landmark)



          Subject:









          As a new recruit in the world of Geo-statistics, I feel a bit unsure on
          what question to ask first.

          I am currently working on a project to evaluate the safety of landmine
          fields. I am therefore mainly interested in the estimation of the completely
          unknown "contamination" level of the field. The variable of interest is discrete
          (landmines) and the populations I will study range from 1000 m2 to 100 million
          m2.

          I have approached the issue by classical random sampling methods (somehow
          inconvenient, but feasible). Unfortunately, to ensure with reasonable confidence
          rates of contamination as low as 10-8, I face sample sizes of nearly 100%.

          What can I do? Can someone help me with the following questions:
          1. How can I tackle this problem of extremely low rates of contamination?
          2. Will Bayesian methods be of any use ? And what books can you recommend
          (easy reading please!)
          3. What about Kriging? I know nothing about it yet, but is it worth
          exploring?

          Many thanks,

          Edith

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