5a Bayesian Approaches - Bayesian Approaches to Perception...

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    Bayesian Approaches to  Perception Randy L. Diehl and Sarah C. Sullivan University of Texas at Austin
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    Rev. Thomas Bayes (1702-1761)
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    Bayesian Statistical Decision Theory  (Ideal Observer Theory) Describes how to perform a perceptual or cognitive task optimally, given the available information and any constraints that apply.
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    Kinds of tasks for which ideal observers  have been derived Coding Detection Discrimination Estimation Object recognition Categorization Navigation
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    A simple categorization task Assume there are n stimulus categories c 1 , c 2 ,…, c n , and the observer’s task is to identify the category, given a particular stimulus S . The optimal decision rule is: ( 29 ( 29 i j p c p c S S If for all j i , then pick c i Posterior probabilities
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    How are these posterior probabilities  calculated? Bayes’ Theorem
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    Bayes’ Theorem  ( 29 ( 29 ( 29 ( 29 i i i p c p c p c p = S S S An Essay Towards Solving a Problem in the Doctrine of Chances . Philosophical Transactions of the Royal Soc. of London,
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5a Bayesian Approaches - Bayesian Approaches to Perception...

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