Inverse probability
Inverse probability [ edit ] In probability theory and applications, Bayes' rule relates the odds of event � 1 to event � 2 , before (prior to) and after (posterior to) conditioning on another event � . The odds on � 1 to event � 2 is simply the ratio of the probabilities of the two events. When arbitrarily many events � are of interest, not just two, the rule can be rephrased as posterior is proportional to prior times likelihood , � ( � | � ) ∝ � ( � ) � ( � | � ) where the proportionality symbol means that the left hand side is proportional to (i.e., equals a constant times) the right hand side as � varies, for fixed or given � (Lee, 2012; Bertsch McGrayne, 2012). In this form it goes back to Laplace (1774) and to Cournot (1843); see Fienberg (2005). See Inverse probability and Bayes' rule . Summary of probabili...