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Appendix D - Dealing with Uncertainty 230
that the hypothesis is true.
Absence of Evidence
The absence of evidence is different from not knowing if the evidence is
present or not, and can be used to reduce the probability of a hypothesis.
The standard formula for updating the odds of a hypothesis, H, given that
evidence, E, is absent is:
O(H/~E) = D * O(H)
where O(H/~E) is the odds of H given the absence of E, and D is the denies
weigth of E. The definition of D is:
D = P(~E/H) / P(~E/~H)
or
D = (1 - P(E/H)) / (1 - P(E/~H))
This is the ratio of probabilities that the evidence is not there when the
hypothesis is true to when the hypothesis is false; i.e. given the evidence is
absent, how likely is is that the hypothesis is true.
Uncertain Evidence
To refelect uncertainty in E, we scale both A and D to A’ and D’ respectively
using linear interpolation. The expressions used to calculate interpolated
values are:
A’ = [2(A-1) * P(E)] + 2 - A
D’ = [2(1-D) * P(E)] + D
While P(E) is greater than 0.5 we use the affirms weigth, and when P(E) is
less than 0.5, we use the denies weigth.
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