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The Perception of Probability (talk recording available)
Dr. Charles Randy Gallistel
Tuesday, March 12, 2013, 01:00pm - 02:00pm
Rutgers University, Department of Psychology and Center for Cognitive Science
When subjects estimate the p parameter of a non-stationary hidden Bernoulli process (e.g., the proportion of green balls in an urn containing red and green balls, with unpredictable silent urn substitutions that change the proportion), they do not update their estimate observation by observation (ball by observed ball), as extant theories predict they should. Instead, they make stepwise changes. The joint distribution of step widths and step heights cannot be explained by a model that assumes a difference threshold on the output (i.e., subjects don't want to bother to make a change every trial, so they only do so when there has been a nontrivial change in their estimate). Pace Prospect Theory, their estimates are accurate over the entire range of probabilities and the precision of their estimates, when properly measured, is the same everywhere. They detect largish changes with a short latency, a high hit rate, and a low false alarm rate. They have second thoughts about some of those changes after seeing more data. I present a simple Bayesian computational model of the perceptual process, with only 2 free parameters, which reproduces subjects' behavior, including the joint distribution of step widths and step heights, the change-detection statistics and the second thoughts. The model illustrates why and how future information may change our previous representation of a past state of the world. I suggest reasons why similar models may apply to a wide range of percepts.