Prediction of Occurrence of Discrete Events - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 177

One of the basic rules of WofE is that the binary patterns selected for further
work should be approximately conditionally independent. A number of conditional
independence tests are in existence ( cf. Thiart et al. 2006 ). An overview of how one
should proceed in the application of WofE is provided in the topic by Bonham-
Carter ( 1994 ). Basically, there are two CI tests: one for pair-wise comparisons of
map layers, and the other (the omnibus test) for comparing sum of posterior
probabilities to total number of mineral deposits. These two totals are approxi-
mately equal when the assumption of conditional independence is satisfied. The
statistical CI test of Agterberg and Cheng ( 2002 ), which was applied earlier in this
section, will be discussed in more detail in the next section. As an artificial example
to illustrate lack of CI, these authors presented duplication of a map layer with
positive weight of 2. This creates posterior probabilities that are more than seven
times too large, because this map layer then receives a weight of 4 instead of 2 (and
e 2 7.39). In situations of this type, WLR automatically compensates for lack of

conditional independence.
Suppose that WofE is applied using a 0.01 km 2 unit cell and color the resulting
posterior probability map using red for the 2 % largest posterior probabilities. If
resolution does not present a problem, one could equally well select a 100 m 2 unit
cell. All posterior probabilities then would become approximately 100 times smaller
but the colored map would stay approximately the same as long as the colors
correspond to percentage values for ranked posterior probabilities. Although there
now are now 100 times as many cells in the maximum 2 % probability class, the area
that is colored red remains approximately the same in this artificial example.
In WofE or WLR it is not necessary to randomly select a set of training cells. If
the unit cell is sufficiently small, any large number of randomly selected training
cells would produce a posterior probability map that is approximately the same as
the map of posterior probabilities for the cells not used in training. The three
probability maps for training, testing and total area are approximately the same.
Consequently, it is not necessary to use a grid as is used in these experiments for the
Gowganda area. Map patterns are either spatially continuous (e.g., Fig. 5.24a, b ), or
discontinuous (geology in Fig. 5.24 ). Continuous patterns may be subjected to
minor discretization if their values are to be used for statistical analysis. Significant
differences, between values of cells for the same variable, are likely to adversely
affect statistical analysis results if training and testing area are geographically
distinct as in Experiments 3-5. This is because other values as well as combinations
of values of variables are likely to exist outside the training area.
For example, suppose that a geophysical variable is restricted to 0-10 range in
the training area where it receives a weighting coefficient, but that in part of the
testing area its values exceed 100. Consequently, its contribution to expected value
in this part of the testing area becomes more than 10 times as large when the same
weighting coefficient is used, and predictions probably are meaningless. Regional
trends in other continuous variables may aggravate the situation. Discretization to
ternary or binary form then would improve results because the possibility of

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