Table 1

Interpretation and formulae for various probabilistic measures

MeasureInterpretationFormula
Probability (eg, of an eventEmbedded Image )A measure of the likelihood of an event. It takes a number between 0 (impossible) and 1 (certain). Embedded Image
Probability of a complementary event (eg, Embedded Image )A measure of the likelihood that an event will not occur. Embedded Image
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. Embedded Image
Bayes’ theoremBayes’ theorem describes the probability of an event (eg,Embedded Image ) based on prior knowledge (eg, event B) of conditions that might be related to the eventEmbedded Image . Embedded Image
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. Embedded Image
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. Embedded Image
Likelihood ratioThe 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). Embedded Image
  • 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.