Dissecting Bayes: Using influence measures to test normative use of probability density information derived from a sample test

by Keiji Ota, Laurence T. Maloney

Bayesian decision theory (BDT) is frequently used to model normative performance in perceptual, motor, and cognitive decision tasks where the possible outcomes of actions are associated with rewards or penalties. The resulting normative models specify how decision makers should encode and combine information about uncertainty and value –step by step–in order to maximize their expected reward. When prior, likelihood, and posterior are probabilities, the Bayesian computation requires only simple arithmetic operations: addition, etc. We focus on visual cognitive tasks where Bayesian computations are carried out not on probabiliti es but on (1)probability density functions and (2) these probability density functions are derived fromsamples. We break the BDT model into a series of computations and test human ability to carry out each of these computations in isolation. We test three necessary properties of normative use of pdf information derived from a sample –accuracy,additivity andinfluence. Influence measures allow us to assess how much weighteach point in the sample is assigned in making decisions and allow us to compare normative use (weighting) of samples to actual, point by point. We find that human decision makers violate accuracy and additivity systematically but that the cost of failure in accuracy or additivity would be minor in common decision tasks. However, a comparison of measured influence for each sample point with normati...

Source: PLoS Computational Biology - May 1, 2024 Category: Biology Authors: Keiji Ota Source Type: research