Prediction of Occurrence of Discrete Events - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 139

Chapter 5
Prediction of Occurrence of Discrete Events
Abstract Many geological bodies or events including various types of mineral
deposits, earthquakes and landslides can be represented as points on small-scale
maps. Various methods exist to express probability of occurrence of such events in
terms of various map patterns based on geological, geophysical and geochemical
data (Agterberg 1989a). The machine-based approach was greatly facilitated by the
development of Geographic Information systems (GIS, cf . Bonham-Carter 1994 ).
Weights-of-Evidence modeling and weighted logistic regression are two powerful
methods useful for estimating probabilities of occurrence of an event within a small
unit area. Weights-of-Evidence (WofE) consists of first assuming that the event can
occur anywhere within the study area according to a completely random Poisson
distribution model. This equiprobability assumption provides the prior probability
that only depends on size of an arbitrarily small unit area. Various indicator map
patterns commonly reduced to binary (presence-absence) or ternary (presence-
absence-unknown) form are used to update this prior probability by means of
Bayes' rule in order to create a map of posterior probabilities that is useful for
selecting target areas for further exploration for undiscovered mineral deposits or
for the prediction of occurrence of other discrete events such as earthquakes or
landslides. If probabilities are transformed into logits, Bayes' rule is simplified: the
posterior logit simply is equal to the sum of the prior logit and the weights of which
there is only one for each map layer at the same point. These weights are either
positive (W + ) or negative (W ) depending on presence or absence of the indicator,
or zero for missing data. An important consideration in WofE applications is that
the indicator patterns should be approximately conditionally independent (CI).
WofE will be illustrated by applications to gold deposits in Meguma Terrain,
Nova Scotia, and to flowing wells in the Greater Toronto area. Weighted logistic
regression (WLR) also can be used to estimate probabilities of occurrence of
discrete events. Both WofE and WLR are applied to gold occurrences in the
Gowganda area on the Canadian Shield, northern Ontario, and to occurrences of
hydrothermal vents on the East Pacific Rise. Indicator patterns used include favor-
able rock types, proximity to anticlinal structures or contacts between rock units,
indices representing various geochemical elements, proximity to lineaments and