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AI-GEOSTATS: Statistics book

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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 1 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 2 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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