Direct Probabilities
Harold Jeffreys · 1998
Abstract where by the likelihood we understand the probability that the observations should have occurred, given the hypothesis and the previous knowledge. The prior probability of the hypothesis has nothing to do with the observations immediately under discussion, though it may depend on previous observations. Consequently the whole of the information contained in the observations that is relevant to the posterior probabilities of different hypotheses is summed up in the values that they give to the likelihood. In addition, if the observations are to tell us much that we do not know already, the likelihood will have to vary much more between different hypotheses than the prior probability does. Special attention is therefore needed to the discussion of the probabilities of sets of observations given the hypotheses.