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Vision Res. 2016 May;122:105-123. doi: 10.1016/j.visres.2016.02.002. Epub 2016 May 2.

Painfree and accurate Bayesian estimation of psychometric functions for (potentially) overdispersed data.

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Neural Information Processing Group, University of Tübingen, Tübingen, Germany; Department of Psychology, Universität of Potsdam, Potsdam, Germany; Graduate School for Neural and Behavioural Sciences IMPRS, Tübingen, Germany. Electronic address:
Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, Germany.
Research Center Caesar, Bonn, Germany; Max Planck Institute for Biological Cybernetics, Tübingen, Germany; Bernstein Center for Computational Neuroscience, Tübingen, Germany.
Neural Information Processing Group, University of Tübingen, Tübingen, Germany; Bernstein Center for Computational Neuroscience, Tübingen, Germany; Max Planck Institute for Intelligent Systems, Tübingen, Germany. Electronic address:


The psychometric function describes how an experimental variable, such as stimulus strength, influences the behaviour of an observer. Estimation of psychometric functions from experimental data plays a central role in fields such as psychophysics, experimental psychology and in the behavioural neurosciences. Experimental data may exhibit substantial overdispersion, which may result from non-stationarity in the behaviour of observers. Here we extend the standard binomial model which is typically used for psychometric function estimation to a beta-binomial model. We show that the use of the beta-binomial model makes it possible to determine accurate credible intervals even in data which exhibit substantial overdispersion. This goes beyond classical measures for overdispersion-goodness-of-fit-which can detect overdispersion but provide no method to do correct inference for overdispersed data. We use Bayesian inference methods for estimating the posterior distribution of the parameters of the psychometric function. Unlike previous Bayesian psychometric inference methods our software implementation-psignifit 4-performs numerical integration of the posterior within automatically determined bounds. This avoids the use of Markov chain Monte Carlo (MCMC) methods typically requiring expert knowledge. Extensive numerical tests show the validity of the approach and we discuss implications of overdispersion for experimental design. A comprehensive MATLAB toolbox implementing the method is freely available; a python implementation providing the basic capabilities is also available.


Bayesian inference; Beta-binomial model; Confidence intervals; Credible intervals; Non-stationarity; Overdispersion; Psychometric function; Psychophysical methods

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