Proceedings of the Annual Meeting of the Cognitive Science Society

We tested three fundamental properties of Bayesian Decision Theoryaccuracy, additivity, and sufficiency. In Experiment1, observers were shown a sample of dots from a bivariate Gaussian and estimate the probability that an additional samplewould fall into specified regions. There were three types of regions: symmetric around the mean (S), the upper andlower halves of the symmetric region (SU and SL). In Experiment 2, the same observers were asked to maximize theexpected rewards based on jointly sufficient statistics for given the sample (herein, mean and covariance of a Gaussian).In Experiment 1, We found that the observers estimates of symmetric region P[S] were close to accurate. However, theyshowed a highly patterned super-additivity: the sum of P[SU] + P[SL] ¿ P[S]. In Experiment 2, the observers violatedsufficiency by assigning too much weight to a feature of the sample rather than jointly sufficient statistics.