I’m not sure what you mean by saying that my Bayesian argument fails in some cases? ‘P(X|E)>P(X) if and only if P(E|X)>P(E|not-X)’ is a theorem in the probability calculus (assuming no probabilities with value zero or one). If the likelihood ratio of X given E is greater than one, then upon observing E you should rationally update towards X.
If you just mean that there are some values of X which do not explain the events of the last week, such that P(events of the last week | X) ≤ P(events of the last week | not-X), this is true but trivial. Your post was about cases where ‘this catastrophe is in line with X thing [critics] already believed’. In these cases, the rational thing to do is to update toward critics.
I’m not sure what you mean by saying that my Bayesian argument fails in some cases? ‘P(X|E)>P(X) if and only if P(E|X)>P(E|not-X)’ is a theorem in the probability calculus (assuming no probabilities with value zero or one). If the likelihood ratio of X given E is greater than one, then upon observing E you should rationally update towards X.
If you just mean that there are some values of X which do not explain the events of the last week, such that P(events of the last week | X) ≤ P(events of the last week | not-X), this is true but trivial. Your post was about cases where ‘this catastrophe is in line with X thing [critics] already believed’. In these cases, the rational thing to do is to update toward critics.