Risk, Unexpected Uncertainty, and Estimation Uncertainty: Bayesian Learning in Unstable Settings
Figure 2
Three kinds of uncertainty in the task.
A Evolution of the estimation uncertainty (entropy of mean posterior outcome probabilities) of chosen options in one instance of the board game. Learning is based on choices of one participant in our experiment. Blue dots on the horizontal axis indicate trials when a blue location was chosen; red dots indicate trials when a red location was visited. B Evolution of the unexpected uncertainty of chosen options in one instance of the board game, measured (inversely) as the probability that no jump has occurred. Learning is based on choices of one participant in our experiment. Blue dots on the horizontal axis indicate trials when outcome probabilities for the visited blue location jumped; red dots indicate trials when outcome probabilities for the visited red location jumped. C Average estimated risk (entropy of outcome probabilities) in one instance of the board game, by location (numbered 1 to 6). Learning is based on the choices of one participant in our experiment. Locations are arranged by level of unexpected uncertainty (blue: low; red: high). Average estimated risks are compared with true risks. The participant managed to distinguish risk differentials across blue locations, but not across red locations. Average estimated risks regress towards the grand mean because of estimation uncertainty after each jump in outcome probabilities.