# Extraordinary claims require extraordinary evidence The odds form of Bayes' rule is written as follows: ![[Bayes' rule — Odds form#^aa9c13]] For the *a priori* improbable proposition that a patient is sick (event $H$) to end up with a higher *a posteriori* probability, the likelihood ratio for the evidence favouring the sick hypothesis, ie, a positive test (event $e$), must be *more extreme* than the prior odds against it. This can happen mostly if $P(e | \neg H)$ is very small, ie, the evidence supporting $H$ is very unlikely if $\neg H$ is true. Hence, "extraordinary evidence". $P(e | H)$ = 1, ie, $e$ having 100% chance of happening if $H$ is true, is actually not that strong an argument to corroborate $H$. Indeed, it is not because it is raining ($e$) in Paris that a giant is crying above me ($H$), since rain is not that unlikely in Paris (ie, $P(e | \neg H)$ is rather high). However, if I am in the desert, then the claim gains credibility (ie, $P(e | \neg H)$, the probability that it rains given that there is no giant, is very low in the desert). ## Corollary Ordinary claims require only ordinary evidence. If you recommended an acquaintance to your company and his manager complains that he does not work well, you are not justified in asking for extraordinary pieces of evidence, since unproductive employees are not that unlikely.