Prediction of Occurrence of Discrete Events - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 181

Fig. 5.28 Seafloor Example. Two of patterns used for to correlate occurrences of 13 hydrothermal
vents on the seafloor (East Pacific Rise, 21 N; based on Fig. 5 of Ballard et al. 1981 ). Top : litho-age
units and vents ( dots ); relative age classes were based on measuring relative amounts of sediments
deposited on top of the volcanics with 1.0-1.4 (youngest), 1.4-17 (intermediate), and 1.7-20
(oldest); Bottom : topography (depth below sea level) (Source: Agterberg et al. 1994 , Plate 1a, b)

probabilities were used by Bonham-Carter et al. ( 2009 ). Schaeben ( 2012 ) has
provided a comprehensive review of all these methods used for mineral resource
appraisal. Cheng ( 2011 ) has developed a boosting version of WofE in which S

N
is nearly satisfied. Boosting (Freund and Schapire 1997 ) consists of sequentially a
classification algorithm to reweighted versions of a set of training data followed by
taking the weighted majority of the sequence of classifiers produced ( cf . Friedman
et al. 2000 ). Deng ( 2009 ) had introduced a conditional dependence adjusted
weights of evidence method. In an application, it was shown this method does not
eliminate bias because it results in S

¼

N but bias is reduced in comparison with
ordinary WofE (Agterberg 2011 ). This existence of bias also has been pointed out
by Schaeben and van den Boogaart ( 2011 ). Schaeben ( 2014 ) has made a detailed
comparison of weights of evidence with logistic regression in terms of Markov
random fields expanding on work by Sutton and McCallum ( 2007 ). However, mit
should be kept in mind that “interpreting regression coefficients can be very tricky”
(Christensen 1990 , p. 259). Agterberg's ( 1989c ) LOGDIA computer program
contains logistic regression diagnostics as developed by Pregibon ( 1981 ). However,
in practical WLR applications, usually is best to evaluate statistical significance by
using the Student's t -map that accompanies the posterior probability map
( cf . Fig. 5.18 ) and the Kolmogorov-Smirnov test (Fig. 5.19 ).
The example of application to be used for illustrating modified WofE here is the
Seafloor Example consisting of 13 volcanic vents on the East Pacific Rise near 21
N (Fig. 5.28 ). It was previously analyzed by means of both WofE and WLR
(Agterberg et al. 1994 ). The datasets used for the current study are slightly different
from those used previously but the new WofE and WLR results are similar to those
derived before and more detailed explanations of input and output patterns can be
found in the earlier papers.

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