Probability and Statistics - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 42

2.1 History of Statistics
Ian Hacking ( 2006 ) has pointed out that the concept of “probability”, which is a
cornerstone of classical statistics, emerged in the middle of the seventeenth century,
gradually assuming its dual objective and subjective meanings ( cf . Agterberg
2013 ). In its objective sense, probability is related to stable experimental frequ-
encies. Subjective frequencies aim to quantify degrees of belief. Advocates of these
two types of probabilities have often disagreed in the past. For example, Ronald
Fisher strongly opposed Bayesians who used Thomas Bayes' rule to update initially
subjective probabilities in an objective manner. His colleague, the geophysicist
Harold Jeffreys, had introduced inductive logic that was later refined by others such
as Bruno de Finetti. To-day, primarily deductive and subjective reasoning both
continue to be practiced. Jef Caers ( 2011 ) argues that “any modeling of uncertainty
is only relevant if made dependent on the particular decision question or practical
application for which such modeling is called for.” Possibility theory as developed
by Didier Dubois and colleagues takes a new type of axiomatic approach in
uncertainty theory (Dubois and Prade 2000 ). In many Bayesian approaches, the
starting point continues to be based on the concept of equipossibility as originally
used by Pierre, Marquis de Laplace.
A simple example of equipossibility followed by deductive reasoning based on
traditional axioms of probability theory is Weights-of-Evidence (WofE) modeling to
estimate probabilities of occurrences of discrete events such as mineral deposits in a
study area. The initial hypothesis of equipossibility is that the probability that a
mineral deposit occurs underneath a small unit area on a map is the same everywhere
within the study area. It gives the prior probability that only depends on size of unit
area. Using Bayes' rule, this prior probability is updated by using as evidence various
features of the unit area that differ from place to place in the study area. The final
WofE product is a map of posterior probabilities for occurrences of mineral deposits.
The geologist Georgius Agricola (in 1556) developed methods of reading signs
on the surface of the Earth such as occurrences of faults or anticlines as indicators
for the occurrence of mineralization. Agricola assumed that “sentences” on the
Earth's surface tell us what minerals are down below. Nevertheless, as Hacking
( 2006 ) points out, Agricola had no idea that there could have been a process of
mineralization that took place millions of years ago. Such concepts had not yet been
developed. It can be argued that the signs identified by Agricola and several others
in the sixteenth century including Paracelsus constituted some early form of
what later became known as “probabilities”. Paracelsus was active in the field of
medicine listing medicines for various illnesses. He developed an early similarity
theory that would not meet standards to be developed later. For example, Paracelsus
wrote: “Do not the leaves of the thistle prickle like needles. Thanks to this sign, the
art of magic discovered that there is no better sign against internal prickling”
(Jacobi 1951 ). The signs of Agricola and Paracelsus were precursors of probabi-
lities. They both knew that the signs they had identified as indicators were not
foolproof either leading to certain discovery of new ore or curing disease with
complete success. In WofE various theories of process-modeling are taken into
account when map layers are selected for improving the posterior probabilities.