Part of Advances in Neural Information Processing Systems 18 (NIPS 2005)
Liam Paninski
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 convex optimization problem (with no non-global local maxima) in many important cases. In addition, we develop methods for analyzing the uncertainty of these esti- mates. We demonstrate the accuracy of the method in a simple simulated coin-flipping setting; in particular, the method is able to precisely track the evolution of the subject’s posterior distribution as more and more data are observed. We close by briefly discussing an interesting connection to recent models of neural population coding.