I am working with long productcs of probabilies and in order of avoinding underflow I am using the addition of (negative) logarithms. P(A) =-log(P(a1) + -log(P(a2)+.... In the end I get a positiv quantity. However, I have a given condition related to the final results. That is, the quotient of the probabilities must be larger than z>1. That is, P(A)/P(B) > z. At the end I have -log(P(A)) and -log(P(B)). How should I adapt my "condition" to the logs? log(P(A)/P(B)) = log(P(A)) - log(P(B)) > log(z) . If I am working with the negated values,I should also invert the innquality log(P(B)) -log(P(A)) < -log(z) But this adaptation seems not to be working. Need help here!
2026-04-11 10:48:12.1775904492
How logarithms affect given condition
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You want $\frac {P(A)}{P(B)} \gt z$ As you say, you can take the log, getting $\log(P(A))-\log(P(B)) \gt \log z$ If you want to express that as negative logs, you want $-(-\log(P(A)))+(-\log(P(B)) \gt -(-\log z)$ Now multiply through by $-1$, remembering to change the sense of the inequality, to get $(-\log(P(A)))-(-\log(P(B)))\lt (-\log z)$