Inferring prior probabilities from Bayes-optimal behavior
To appear,
Neural Information Processing Systems 2005
We discuss a method for obtaining a subject's a priori
beliefs from his/her behavior in a psychophysics context, under the
assumption that the behavior is (nearly) optimal from a Bayesian
perspective. The method is nonparametric in the sense that we do not
assume that the prior belongs to any fixed class of distributions
(e.g., Gaussian). Despite this increased generality, the method is
relatively simple to implement, being based in the simplest case on a
linear programming algorithm, and more generally on a straightforward
maximum likelihood or maximum a posteriori formulation, which
turns out to be a concave maximization problem (with no non-global
local maxima) in many important cases. We explore the variability of
the methods and emphasize the importance of regularization of the
problem, via mathematical analysis and numerical examples. We close
by briefly discussing an interesting connection to recent models of
neural population coding.
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