Table 1

Interpretation and formulae for various probabilistic measures

 Measure Interpretation Formula Probability (eg, of an event  ) A measure of the likelihood of an event. It takes a number between 0 (impossible) and 1 (certain).  Probability of a complementary event (eg,  ) A measure of the likelihood that an event will not occur.  Conditional probability (eg, of an event A given an event B) A measure of the likelihood of an event (eg, A) given that another event (eg, B) has occurred.  Bayes’ theorem Bayes’ theorem describes the probability of an event (eg,  ) based on prior knowledge (eg, event B) of conditions that might be related to the event  .  Prior odds (eg, of an event A) The odds in favour of A; the probability A will occur divided by the probability it will not occur.  Posterior odds (eg, of an event A given that B has occurred) The odds of A in light of B; the probability A will occur given B has occurred divided by the probability A will not occur given that B has occurred. They inform us how odds of A have been updated given that B has occurred.  Likelihood ratio The factor which updates prior odds in favour of an event (eg, A+) to posterior odds in favour of an event in the light of new information (eg, B).  • We use upper indices + and − to denote whether event A happens or not. For event B, we assume that it always happens and we omit the upper index.