If hypothesis A implies that the probability that a random variable X takes the value x is pA(x), while hypothesis B implies that the probability is pB(x), then the observation X = x is evidence supporting A over B if and only if pA(x) > pB(x), and the likelihood ratio, pA(x)/ pB(x), measures the strength of that evidence.’
‘This says simply that if an event is more probable under hypothesis A than hypothesis B, then the occurrence of that event is evidence supporting A over B – the hypothesis that did the better job of predicting the event is better supported by its occurrence.’ Moreover, ‘the likelihood ratio, is the exact factor by which the probability ratio (ratio of priors in A and B) is changed. … Law of Likelihood