Probability matching

Probability matching is a decision strategy in which predictions of class membership are proportional to the class base rates. Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, then the observer using a probability-matching strategy will predict (for unlabeled examples) a class label of 'positive' on 60% of instances, and a class label of 'negative' on 40% of instances. Probability matching is a decision strategy in which predictions of class membership are proportional to the class base rates. Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, then the observer using a probability-matching strategy will predict (for unlabeled examples) a class label of 'positive' on 60% of instances, and a class label of 'negative' on 40% of instances. The optimal Bayesian decision strategy (to maximize the number of correct predictions, see Duda, Hart & Stork (2001)) in such a case is to always predict 'positive' (i.e., predict the majority category in the absence of other information), which has 60% chance of winning rather than matching which has 52% of winning (where p is the probability of positive realization, the result of matching would be p 2 + ( 1 − p ) 2 {displaystyle p^{2}+(1-p)^{2}} , here .6 × .6 + .4 × .4 {displaystyle .6 imes .6+.4 imes .4} ). The probability-matching strategy is of psychological interest because it is frequently employed by human subjects in decision and classification studies (where it may be related to Thompson sampling).