Geoscience Reference
In-Depth Information
Table 5.5 Summary of WLR results for Experiments 1-5
Experiment number
1
2
3
4
5
Constant term, B0
8.8639
7.3394
9.8428
5.7877
9.0784
SD (B0)
1.3241
0.7746
1.9138
1.2414
1.1576
B (Geology)
1.6059
1.6620
2.2080
1.3413
1.2101
SD (Geology)
0.4468
0.2543
0.7606
0.4537
0.3193
B (PC3)
0.1201
0.1492
0.0496
0.1697
0.1081
SD (PC3)
0.0490
0.0281
0.0652
0.0444
0.0423
B (Magnetics)
0.1657
0.0504
0.0064
0.0148
0.3010
SD (Magnetics)
0.0554
0.033
0.0674
0.0523
0.0732
Sum of PPs
23
15
19
24
43
Observed number of deposits (Testing)
67
75
71
66
47
Estimated number of deposits (Testing)
69
43
22
99
198
Smallest PP (Training)
0.0000
0.0002
0.0001
0.0001
0.0001
Largest PP for cell with known deposit
(Training)
0.0303
0.0035
0.0037
0.0296
0.0400
Largest PP for cell without known deposit
(Training)
0.0788
0.0129
0.0047
0.0344
0.0953
Smallest PP (Testing)
0.0000
0.0092
0.0045
0.0303
0.1633
Largest PP for cell with known deposit
(Testing)
0.0312
0.0092
0.0045
0.0303
0.1633
Largest PP for cell without known deposit
(Testing)
0.0788
0.0142
0.0047
0.0349
0.3217
Source: Agterberg and Bonham-Carter ( 2005 , Table 2)
Note: B WLR coefficient, SD standard deviation, PP posterior probability
5.2.4 Results of the Gowganda Experiments
Weights-of-Evidence (WofE) and Weighted Logistic Regression (WLR) results for
the five experiments are summarized in Tables 5.5 and 5.6 . For all five experiments,
the sum of WofE posterior probabilities (the product of probability and area in unit
cells summed over all unique conditions) exceeds the number of deposits in the
training area. This suggests that the assumption of conditional independence may
be violated. However, application of the conditional independence (CI) test of
Agterberg and Cheng ( 2002 ) yields a test statistic with probabilities ranging from
0.569 (Experiment 3) to 0.941 (Experiment 4). Normally, the CI hypothesis would
be rejected only if the probability for this one-tailed z -test exceeds 95 % or 99 %,
corresponding to level of significance set equal to 0.05 or 0.01, respectively.
However, it is unlikely that in five successive experiments none of the CI proba-
bilities are less than 0.5, and some CI violation probably exists. For this reason, all
WofE posterior probabilities were reduced by a factor set equal to the quotient of
number of deposits and sum of WofE posterior probabilities in the training area.
This factor ranges from 0.514 (Experiment 4) to 0.948 (Experiment 3).
Theoretically, the WLR sum of posterior probabilities is exactly equal to number
of deposits in the testing area. In practice, this sum may differ somewhat from
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