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Spatiotemporal Mapping in Natural Sciences 21

criticism of traditional methods has been called "obscurantism" by Whitehead
(1969, p. 43), who writes in a memorable passage, "Obscurantism is the refusal
to speculate freely on the limitations of traditional methods. It is more than
that: it is the negation of the importance of such speculation, the insistence of
incidental dangers."
It is not appropriate to consider geostatistics from the Procrustean view-
point of obscurantism (Procrustes was the ancient mythical giant who chopped
off the legs of travelers when they did not fit his bed). For geostatistics to flour-
ish, it must be allowed to use new concepts and tools freely, unconstrained by
preconceived notions of what geostatistics ought to be. Therefore, the devel-
opments proposed by modern spatiotemporal geostatistics should be viewed in
a non-Procrustean spirit. Certainly, the epistemic approach to modern geo-
statistics discussed in this book is not the only possibility. The book is more
like a "call for research," encouraging a multidisciplinary conception of mod-
ern geostatistics directed toward novel ideas and models which consider the
advances of numerous scientific disciplines where geostatistical ideas can be
applied.

Bayesian Maximum Entropy Space/Time
Analysis and Mapping

The study of the scientific status of spatiotemporal modeling and mapping
forms a group of methods that can be placed in a unified framework demon-
strating its significance to the development of modern geostatistics (Definition
1.1). From the epistemic viewpoint, spatiotemporal mapping is a combination
of both functions of scientific reasoning, namely, the examination of hypotheses
regarding a natural variable and the determination of estimates for the values
of that variable. A particularly important member of this group of methods
is Bayesian maximum entropy (BME) spatiotemporal analysis and mapping
(Christakos, 1990, 1991a, 1992, 1998a, b).
COMMENT 1.4 : Before proceeding an y further, le t u s make a brief note

about the term "BME." The epistemic framework of the new approach in-

volves the concepts of Bayesian conditionalization (see Chapter 4, Eq. 4-9,

p. 96) and entropy (Chapter 5, Eq. 5.2, p. 105), thus the acronym "BME."

For readers who would like to review Bayesian analysis and entropic con-

cepts, good references are the books by Howson and Urbach (1993) and
Robert (1994) and the collection of papers by Jaynes (1983). It should be

kept in mind, however, that the introduction of Bayesian thinking in modern

spatiotemporal geostatistics is epistemically and physically motivated, rather

than merely promoting a statistical methodology. Also, as we shall see be-
low, the modern geostatistics framework is very general and should not be

restricted by such acronyms. Indeed, the Bayesian concept can be general-

ized significantly by means of the knowledge processing rules of mathematical

logic, and information measures other than entropy may be considered.