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

publications.

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.

Karel

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

(vision).

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

estimate.

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

exists.

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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