Prediction of Occurrence of Discrete Events - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 161

exactly known how many undiscovered deposits there are in a region and this
quantity remains unknown. Because the estimated weights depend only on
presence or absence of features at the actual sites of the deposits, the weights
estimated for known and unknown deposits in a region can be assumed to be
independent of the prior probability. In order to hypothetically incorporate
unknown events in the study area, one might change the prior probability by
increasing it by a factor based on intensity of exploration (Agterberg 1992 ). If a
reasonable guess can be made on number of undiscovered deposits, for example
by assuming that all deposits have been discovered in “control” area consisting
of mining districts, then the prior probability can be enlarged accordingly. It
should be kept in mind, however, that most unknown metal resources may well
occur at greater depths within mining districts as was shown for copper in the
Abitibi area in Sect. 4.4.2 .
Another question asked with respect toWofE applications is that reduction of map
layers for indicator variables to binary or ternary form seems to be crude approxima-
tion. WofE software generally allows for approximations with more than two or three
states. An example of application without missing data in which more than two states
are needed are aeromagnetic data in relation to occurrences of earthquakes (Goodacre
et al. 1993 ). Agterberg and Bonham-Carter ( 1990 ) have shown that it is possible to
construct variable weight functions in an application to the relationship between
occurrences of gold deposits and proximity to Devonian anticlines in Meguma
Terrain, Nova Scotia. Variable weights also can be calculated when the input layer
is obtained by 2-D kriging in which the kriging variance strongly depends on density
of observation points as shown by Bonham-Carter and Agterberg ( 1999 ) in a study of
relating the Meguma Terrain gold deposits to Au in balsam fir trees.

5.2 Weighted Logistic Regression

If it is assumed that there are no undiscovered or new events in a study area, the sum
of the posterior probabilities should be, at least approximately, equal to the number of
known events if the conditional independence (CI) assumption is satisfied. Weighted
logistic regression (WLR) yields unbiased posterior probabilities if undiscovered
events are not considered. This technique is equivalent to ordinary logistic regression
except that the input values for the explanatory variables are weighted according to
their areal extents within the study area. Logistic regression coefficients are equiva-
lent to WofE contrasts ( C W ) that measure strength of correlation between

point pattern and map layers. Logistic regression will be applied to occurrences of
volcanogenic massive sulphide and magmatic nickel-copper deposits in the Abitibi
area on the Canadian Shield for comparison with results as obtained in the previous
chapter by means of the general linear model of least squares.

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