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428AI-GEOSTATS: Re: cracks in geostat foundations

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  • Karel Sevcik
    Nov 1, 2001
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      Hi everybody,
      I appreciated extensive discussion on "Cracks in
      geostatistical foundations". Unfortunately, it seems
      like the joke saying "it two lawyers discus a problem,
      they have at least five professional opinions". It
      gives me courage to add one more.
      Geostatistics is developed on a base of some paradigm,
      specifically the Newtonian mechanical paradigm. It
      gives to geostatistcs some advantages and also some
      weaknesses. Geostatistics is not designed for
      inhomogeneous sets, nonstationary sets, sets with
      varying slope, and perhaps many more. Conditions for
      data are defined in Matheron's works and many other
      Problem is not in geostatistics. Problem is in
      application of geostatistics, where it cannot be
      successful. Why to use a hammer for screwing screws?
      Geostatistics really have several theoretical
      problems. Many practical applications may fail, but
      many are completely satisfactory. Solution is simple:
      If geostatistical results are satisfactory, be happy,
      if not, do not cry, but seek better technology.
      It's easy to say, but hard to see it through.
      Fortunately, I can speak like that. If anybody is
      interested in an alternative to geostatistics, please,
      read the following short summary and do not hesitate
      to ask.


      Dr. Karel SEVCIK, Australia, k_sevcik@...
      Knowledge of spatial properties of studied variables
      is fundamental for many scientific fields, from
      geology to for example engineering, information
      technology, automation, economy, and particularly for
      artificial intelligence and artificial sensing
      Although Theory of Regionalized Variable
      (geostatistics) represents significant experiment,
      until now, no modern scientific approach to these
      estimation problems has existed. Gnostical Theory of
      Spatial Uncertain Data (GTSUD or perhaps
      "geognostics"), the principles of which are summarized
      in this abstract constitutes a new generation of
      approaches to quantitative spatial data. Some of the
      main results given by GTSUD are shown and critically
      compared with classical methods of geostatistics.
      GTSUD grows from mathematical properties of space and
      numbers. Each individual datum carries complete
      information. It is considered a unique individual
      object. Spatial datum is composed of two separate
      parts: its uncertain value and spatial location. Each
      part must have structure of a quantitative numerical
      group. Kind of structure of the group completely
      determines data model and space model. Consequently,
      GTSUD is applicable to any quantitative data (measured
      or counted). There is no assumption on data
      distribution or their spatial properties like
      stationarity, homogeneity, trend, etc.
      Natural consequence of existence of information
      uncertainty (i.e. a difference between uncertain
      information value of a datum (e.g. measured ore
      concentration) and its ideal value) is a pair of
      information characteristics: information weight and
      information irrelevance. Because space (or time) is
      also quantitative variable, existence of spatial
      uncertainty (difference between location of a datum
      (sample) and location of an estimate) naturally
      results in existence of a pair of spatial
      characteristics: spatial weight and spatial
      irrelevance. Each individual spatial uncertain datum
      possesses these four characteristics regardless of
      other properties (e.g. geostatistical). There is no
      relationship between information and spatial
      characteristics (e.g. no need for stationarity,
      homogeneity or model distribution).
      Squares of weight and irrelevance have direct physical
      interpretations in growth of entropy and loss of
      information. Entropy and information form two mutually
      compensating fields. The mentioned functions result in
      definition of two distribution functions of an
      individual spatial uncertain datum, one in information
      structure, second for space. Interpretation of all the
      above mentioned functions is completely isomorphic
      with interpretations of corresponding characteristics
      in the Special Theory of Relativity and significant
      correspondence with quantum mechanics was also shown
      in literature.
      Proven additive composition of information weight and
      information irrelevance results in two kinds of
      distribution functions: global distribution (GDF) and
      local distribution (LDF). Although spatial weight and
      spatial irrelevance are also additive, they are not
      used in estimation of "spatial distribution", but in
      contrast, they serve for optimization of distribution
      estimates of the observed variable at a point of an
      Global distribution function is very robust and
      describes data as one cluster (homogeneous). It has no
      general statistical counterpart. Field of GDF-estimate
      over studied space is always unimodal, but need not be
      continuous and partially need not exist at all. If
      data are not homogeneous in their value in some area,
      this estimate simply does not exist. Practical
      consequence is: (1) in protection of the estimate
      against influence of inhomogeneity like e.g. nugget
      effect and consequent extreme robustness; and (2) in
      detection of spatial discontinuity in values like e.g.
      faults or different geochemical units. There is no
      need for any kind of test of existence of GDF, because
      it always does not exist, if at least one point of its
      derivative (the data density) is negative (general
      probabilistic definition of distribution function).
      Local distribution function is infinitely flexible and
      thus it could describe multimodal data. Its
      statistical counterpart could be found in Parzen's
      kernels. Practical consequence is: (1) in separation
      of different objects like e.g. one map for main
      concentration field and separate maps of nuggets,
      pollution, leached zones in a single estimate; and (2)
      in detection of spatial discontinuity in values like
      e.g. faults or different geochemical units. There is
      also no need for testing, because this estimate always
      Quality of estimates is measured by growth of entropy
      and loss of information, what guarantees best possible
      results. GTSUD extracts maximum information from data,
      but cannot "make" more information, than information
      contained in data.
      GTUSD produces simple, universal and strictly logic
      algorithms easily programmable for computers. Such
      programs are applicable to any data without need for
      special knowledge or human interference, like
      "art-of-geostatistics". Properties of GTSUD protect
      applications from production of mistaken results (e.g.
      if data are inhomogeneous in their values at one
      point, there is preferred no result for that point
      against wrong global estimate, while local estimate
      always exists, but might have more than one value).

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