It looks hideous written out that way (assuming I even wrote it correctly) but the way I visualize it is nice and intuitive. I actually translate probabilities into odds ratios in my head and back whenever I try to do probability calculations. It feels more natural somehow.
I usually use the odds ratio formulation because it’s easier for me to remember and intuitively grok.
P(A|E) / P(~A|E) = P(A) / P(~A) * P(E|A) / P(E|~A)
It looks hideous written out that way (assuming I even wrote it correctly) but the way I visualize it is nice and intuitive. I actually translate probabilities into odds ratios in my head and back whenever I try to do probability calculations. It feels more natural somehow.
A’s odds under E equal As usual odds times E’s odds under A?
Yes. E as in evidence.