Probability matching is a

decision strategy Decision theory (or the theory of choice; not to be confused with Rational choice theory, choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors an ...

in which predictions of class membership are proportional to the class

base rates In probability and statistics, the base rate (also known as prior probabilities) is the class of probabilities unconditional on "featural evidence" (likelihoods). For example, if 1% of the population were medical professionals, and remaining 9 ...

. 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 ) 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

, here

.6 \times .6+ .4 \times .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 Thompson sampling, named after William R. Thompson, is a heuristic for choosing actions that addresses the exploration-exploitation dilemma in the multi-armed bandit problem. It consists of choosing the action that maximizes the expected reward wi ...

). The only case when probability matching will yield same results as Bayesian decision strategy mentioned above is when all class base rates are the same. So, if in the training set positive examples are observed 50% of the time, then the Bayesian strategy would yield 50% accuracy (1 × .5), just as probability matching (.5 ×.5 + .5 × .5).

References

* * Shanks, D. R., Tunney, R. J., & McCarthy, J. D. (2002). A re‐examination of probability matching and rational choice. ''Journal of Behavioral Decision Making'', 15(3), 233-250. Statistical classification Machine learning Decision-making Cognitive science Cognitive biases {{statistics-stub