This conversation piqued my interest because one of my expectations was subverted. Due to habits ingrained in me while applying Bayes’ theorem in more formal statistical inference, I almost never give consideration to P(B) in these informal applications; I find it much easier to think about the likelihood ratio, P(B given A) / P(B given not-A).
Given P(A), the likelihood ratio determines P(B) and vice versa, so it’s not like there’s any difference in practice. But I find it interesting to observe a different habit of mind in action.
This conversation piqued my interest because one of my expectations was subverted. Due to habits ingrained in me while applying Bayes’ theorem in more formal statistical inference, I almost never give consideration to P(B) in these informal applications; I find it much easier to think about the likelihood ratio, P(B given A) / P(B given not-A).
Given P(A), the likelihood ratio determines P(B) and vice versa, so it’s not like there’s any difference in practice. But I find it interesting to observe a different habit of mind in action.
It is interesting. I (informally) use P(A)*P(B|A) / [ P(B|A)+P(B|notA) ].