AI-GEOSTATS: Re: cracks in geostat foundations
- 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
SUMMARY OF GNOSTICAL THEORY OF SPATIAL UNCERTAIN DATA
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
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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