How to Measure Evidence: Bayes Factors or Relative Belief Ratios?

One of the virtues of the Bayesianapproachto statistical analysisis that it gives an unambiguous definition of what it means for there to be evidence in favor of or against a particular value of a parameter. This is provided by the following principle. Principle of Evidence: if the posterior probability of an event is greater than (less than, equal to) its prior probability, then there is evidence in favor of (against, no evidence either way of) the event being true. This seems like a very simple and intuitively satisfying way of characterizing evidence and it has long been considered to be quite natural and obvious. For example, Popper (1968) The Logic of Scientific Discovery, Appendix ix "If we are asked to give a criterion of the fact that the evidence y supports or corroborates a statement x, the most obvious reply is: that y increases the probability of x." Achinstein (2001) "for a fact e to be evidence that a hypothesis h is true, it is both necessary and sufficient for e to increase h's probability over its prior probability".