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AI-GEOSTATS: Interpretation of nugget effect

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  • Peter Pinn
    Hello everybody, I have several (maybe too simple) questions on geostatistics: 1. I would like to know where I can find any kind of detailed interpretation
    Message 1 of 3 , Aug 19 4:48 AM
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      Hello everybody,

      I have several (maybe too simple) questions on geostatistics:

      1. I would like to know where I can find any kind of detailed interpretation
      guide for the nugget effect. I know how to describe the nugget effect in my
      words, but I don�t know how do it in scientific english.

      2. I do have count data from a regular sampling grid which is in my eyes to
      sparse. Can I refer to the nugget effect to demonstrate this ?

      3. I would like to know more about the sensitivity of kriging for non-normal
      distributed datasets. I have distributions from my above mentioned count
      data which have more or less 80% zeros. Is this problematic when working
      with kriging (and why???).

      4. Is ist really practicable to transform the above mentioned datasets with
      many zeros in it into a lognormal distribution (log = err !!!) ?

      Hopefully anybody out there can help me understanding this better...

      Peter Pinn

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    • Ruben Roa Ureta
      ... nugget effect in my words, but I don´t know how do it in scientific english. ... mentioned count data which have more or less 80% zeros. Is this
      Message 2 of 3 , Aug 19 11:57 AM
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        > Hello everybody,
        >
        > I have several (maybe too simple) questions on geostatistics:
        >
        > 1. I would like to know where I can find any kind of detailed
        > interpretation guide for the nugget effect. I know how to describe the
        nugget effect in my words, but I don´t know how do it in scientific
        english.
        >
        > 2. I do have count data from a regular sampling grid which is in my eyes
        > to sparse. Can I refer to the nugget effect to demonstrate this ?
        >
        > 3. I would like to know more about the sensitivity of kriging for
        > non-normal distributed datasets. I have distributions from my above
        mentioned count data which have more or less 80% zeros. Is this
        problematic when working with kriging (and why???).

        From an empirical point of view: i often meet data with lots of zeros when
        i do gs from samples taken by ships during marine ecology surveys. I have
        done the analysis (both the structural part and kriging) with and without
        the zeros without much of a difference.

        > 4. Is ist really practicable to transform the above mentioned datasets
        > with many zeros in it into a lognormal distribution (log = err !!!) ?

        There is a generalization of the lognormal distribution which accounts for
        the presence of zeros. It is called the Delta distribution. IIRC, the
        maximum likelihood estimate of the lognormal mean (l) is related to the
        mle of the delta mean (d) by the simple relation d=l*(m/n) where m is the
        number of non zero observations and n is the total number of observations.

        Here you have two useful references:
        Aitchison J. 1955. On the distribution of positive random variables having
        a discrete probability mass at the origin. J. American Statistical
        Association 50:901. (Aitchison and Brown wrote the first basic book on the
        lognormal).
        Pennington M. 1983. Efficient estimators of abundance, for fish and
        plankton surveys. Biometrics 39:281. (this work deals specifically with
        the problem of large number of zeros and the lognormal pdf).
        Good luck.
        Ruben

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