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AI-GEOSTATS: Statistics book

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  • Digby Millikan
    Hello, I was wondering if some one could reccomend a book on statistics which covers the basic theories of probability (expectations), least squared errors and
    Message 1 of 5 , Nov 25, 2002
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      Hello,
      I was wondering if some one could reccomend a book on statistics which covers the
      basic theories of probability (expectations), least squared errors and lagrange multipliers
      for understanding the derivation of kriging equations which can be found in many texts.
      Regards Digby Millikan.

      I have searched the Internet and found the Schaums books which I might have a look at,
      Thanks
      Regards Digby Millikan

      [Non-text portions of this message have been removed]
    • Digby Millikan
      Thanks Donald, I ll look into these. Regards Digby Millikan. ... From: Donald E. Myers To: Digby Millikan Sent: Tuesday, November 26, 2002 4:24 AM Subject: Re:
      Message 2 of 5 , Nov 26, 2002
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        Thanks Donald, I'll look into these.

        Regards Digby Millikan.
        ----- Original Message -----
        From: Donald E. Myers
        To: Digby Millikan
        Sent: Tuesday, November 26, 2002 4:24 AM
        Subject: Re: AI-GEOSTATS: Statistics book


        The Schaumns Outline book on Probability is not a bad place to start but I
        think it does not include much about continuous probability distributions.
        There is a book by Miller and Freund on engineering statistics that is not
        a bad choice for the rudiments of probability and statistics. Both of these
        would provide some background on the expected value of a random variable
        (however I think that the Schaums Outline book will only consider discrete
        distributions)

        As for Lagrange multipliers, that is not really a part of either
        probability theory or statistics, it is a part of optimization theory. You
        will find some discussion of them in books on matrix theory, particularly
        related to eigenvalue problems and maximization/minimization of quadratic
        expressions (I think there is a Schaums Outline book on matrix theory)
        subject to a constraint. In the case of the kriging equations, the
        constraint is unbiasedness of the estimator.

        With respect to "least squares", there are two senses to this. One
        corresponds to fitting data to a function via least squares, this is
        essentially deterministic. The second is more like what happens in the
        derivation of the kriging equations, i.e., a certain expected value is
        minimized.

        Donald E. Myers
        http://www.u.arizona.edu/~donaldm

        Digby Millikan wrote:

        Hello,
        I was wondering if some one could reccomend a book on statistics which
        covers the
        basic theories of probability (expectations), least squared errors and
        lagrange multipliers
        for understanding the derivation of kriging equations which can be found
        in many texts.
        Regards Digby Millikan.

        I have searched the Internet and found the Schaums books which I might
        have a look at,
        Thanks
        Regards Digby Millikan



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      • Digby Millikan
        Thanks Isobel, I have purchased and am reading Practical Geostatistics 2000 at the moment, but as it is a few years since I took maths and statistics courses I
        Message 3 of 5 , Nov 26, 2002
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          Thanks Isobel,

          I have purchased and am reading Practical Geostatistics 2000 at the moment,
          but as it is a few years since I took maths and statistics courses I was
          going to
          review the basic principles to understand the derivation of kriging
          equations,
          but not until I have read your book.

          Regards Digby Millikan.


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        • Digby Millikan
          Hello, Here is a summary of responses to my posting, thanks to Donald for his most informative summary, and Isobel for her book which I am reading.
          Message 4 of 5 , Nov 29, 2002
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            Hello,

            Here is a summary of responses to my posting, thanks to Donald for his most
            informative
            summary, and Isobel for her book which I am reading.

            //=================================================================
            Hello,
            I was wondering if some one could recommend a book on statistics which
            covers the
            basic theories of probability (expectations), least squared errors and
            lagrange multipliers
            for understanding the derivation of kriging equations which can be found in
            many texts.
            Regards Digby Millikan.

            I have searched the Internet and found the Schaums books which I might have
            a look at,
            Thanks
            Regards Digby Millikan

            //=================================================================
            The Schaumns Outline book on Probability is not a bad place to start but I
            think it does not include much about continuous probability distributions.
            There is a book by Miller and Freund on engineering statistics that is not
            a bad choice for the rudiments of probability and statistics. Both of these
            would provide some background on the expected value of a random variable
            (however I think that the Schaums Outline book will only consider discrete
            distributions)

            As for Lagrange multipliers, that is not really a part of either probability
            theory or statistics, it is a part of optimization theory. You will find
            some discussion of them in books on matrix theory, particularly related to
            eigenvalue problems and maximization/minimization of quadratic expressions
            (I think there is a Schaums Outline book on matrix theory) subject to a
            constraint. In the case of the kriging equations, the constraint is
            unbiasedness of the estimator.

            With respect to "least squares", there are two senses to this. One
            corresponds to fitting data to a function via least squares, this is
            essentially deterministic. The second is more like what happens in the
            derivation of the kriging equations, i.e., a certain expected value is
            minimized.

            Donald E. Myers
            http://www.u.arizona.edu/~donaldm
            //=================================================================
            Digby

            What's wrong with Practical Geostatistics 2000?
            Isobel
            //=================================================================







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          • Isobel Clark
            Hi Digby The short answer to your least squares question is because Matheron was a least squares person ;-) There are three basic schools of statistics: (1)
            Message 5 of 5 , Nov 29, 2002
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              Hi Digby

              The short answer to your least squares question is
              'because Matheron was a least squares person' ;-)

              There are three basic schools of statistics:

              (1) least squares (sometimes known as frequentist)
              which probably includes the majority of
              non-statisticians doing statistics. The least squares
              approach might be paraphrased as "closest to the real
              answer on average". It is based on the concept of
              approximately Normal 'errors'

              (2) maximum likelihood. This could be paraphrased as
              'that solution from which the samples are most likely
              to have come'. This yields much more general but not
              always unbiassed answers. For example, the maximum
              likelihood estimator of the variance is divided by 'n'
              not 'n-1' as in least squares. Maximum likelihood
              demands a pretty fair knowledge of the underlying
              distribution of the samples, not the errors as such.

              (3) bayesian estimation. Based somewhat on a maximum
              likelihood method, you can build in your own prior
              knowledge about the situation to affect the final
              answers. (1) and (2) above rely solely on hard data.

              This is, of course, a massive over-simplification but
              serves, I think, to emphasise why there are many
              different answers to the same problem and why you have
              to define what you mean by "best" before you get the
              "best answer". I try to cover these concepts in
              non-rigorous terms in all my teaching.

              It is also true that the mathematics is much simpler
              if you use variances than if you use any other
              function of differences.

              Isobel
              http://geoecosse.bizland.com/news.html


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