Let $P(U) = 0.002$, $P(U \mid c) = 0.04$, and $P(c) = 0.05$. Then $P(U \mid \lnot c) = (0.002 - 0.04\cdot0.05) / (1 - 0.05) = 0$. With these values, POM VOI comes out as 0.418 but the VoI_PoM function returns NaN.
This is because the KL function doesn't take into account the edge cases where either p==0 or p==1. In these cases, the corresponding term should be interpreted as 0 (source).
There is an argument to be made that if $P(U \mid \lnot c) = 0$, the forecast could be interpreted as incoherent; for the questions we're asking, saying that the probability of the ultimate question is 0 is a very strong claim. But I don't think we should make that judgment in this package.
Let$P(U) = 0.002$ , $P(U \mid c) = 0.04$ , and $P(c) = 0.05$ . Then $P(U \mid \lnot c) = (0.002 - 0.04\cdot0.05) / (1 - 0.05) = 0$ . With these values, POM VOI comes out as 0.418 but the
VoI_PoMfunction returnsNaN.This is because the
KLfunction doesn't take into account the edge cases where eitherp==0orp==1. In these cases, the corresponding term should be interpreted as 0 (source).There is an argument to be made that if$P(U \mid \lnot c) = 0$ , the forecast could be interpreted as incoherent; for the questions we're asking, saying that the probability of the ultimate question is 0 is a very strong claim. But I don't think we should make that judgment in this package.