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Re: AI-GEOSTATS: Statistics book

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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 1 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
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