Page 11 - Modern Spatiotemporal Geostatistics
P. 11

x              Modern Spatiotemporal   Geostatistics

         a  deeper understanding  of  a theory  of  knowledge is an  important  prerequisite
         for the development of improved mathematical models of scientific  mapping.  A
         spatiotemporal  map, e.g., should depend on what  we know about  the  natural
         variable it  represents, as well as how we know it (i.e., what sources of  knowledge
         we  selected and what  kinds of  methods we  used  to  process  knowledge).  As is
         discussed in the  book,  modern geostatistical  approaches can be developed that
         are consistent with the above epistemic framework.  The main focus of the  book
         is the  Bayesian  maximum entropy  (BME)  approach for  studying  spatiotempo-
         ral  distributions  of  natural  variables.  As  part  of  the  modern  spatiotemporal
         geostatistics  paradigm, the  BME  approach provides a fundamental insight into
         the  mapping  problem  in  which  the  knowledge of  a  natural  variable,  not  the
         variable  itself,  is the  direct  object  of  study.  This  insight  plays a central  role in
         numerous scientific  disciplines.  BME's  rich theoretical  basis provides guidelines
         for  the  adequate interpretation  and  processing of  the  knowledge  bases  avail-
         able  (different  sorts of  knowledge enter the  modern  geostatistics  paradigm in
         different  ways).  It  also  forces  one to  determine  explicitly  the  available  physi-
         cal  knowledge  bases  and to  develop  logically  plausible  rules  and standards  for
         knowledge  integration  and  processing.  BME  is formulated  in  a  rigorous  way
         that  preserves earlier geostatistical  results, which are its limiting cases, and also
         provides  novel and more general results that could  not  be obtained  by classical
         geostatistics.  Indeed, a number of situations are discussed in the  book in which
         BME's  quest  for  greater  rigor  serves  to  expose new, hitherto  ignored  possibil-
         ities.  In  addition,  the  presentation  of  the  quantitative  results, with  their  full
         technical  beauty, is combined with an effort  to  communicate across the various
         fields of  natural science.  Finally, an attempt  has been  made to  ensure that  the
         case studies considered in this book involve data that are publicly  accessible,  so
         that all  hypotheses made and conclusions  drawn can be critically examined and
         improved  by others  (in  fact,  a scientific  model gains authority  by  withstanding
         the  criticism  of  other  scientists).  Naturally,  ideas and practical suggestions on
         how to  efficiently  apply  BME  theory will evolve as more case studies are done.
             Metaphorically  speaking,  the  aim of  modern spatiotemporal  geostatistics
         is to  integrate  effectively the powerful theoretical perspective of the  "Reason of
         Plato"  (who  proposed a conceptual framework that  dominated  mathematical
         reasoning and philosophical thinking for  thousands of years) with the  practical
         thinking  of  the  "Reason  of  Odysseus"  (who  was  always  capable  of  coming
         up with  smart  solutions  to  all  kinds of  practical  problems he faced during his
         long journey).  It  has been  said that  "Plato  shared  his  perspective with  the
         Gods and Odysseus with the foxes."  The  modern geostatistician  shares it with
         both!  At  this  point,  I  must  admit  to  using these great  men as a  provocative
         and  authoritative  means of setting things up and getting readers into the right
         mood.
             In light of the above considerations, the Ariadne's thread running  through-
         out the  book is that the modern geostatistical  approach to  real-world problems
         is that of natural scientists who are more interested  in a stochastic analysis con-
         cerned with  both  the  ontological  level (building  models for  physical systems)
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