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Decision-making out of neural events: from discrimination information to psychometric power laws

The strength/intensity of the stimulus in the random dot motion task (RDMT) [1] is determined by the percentage of dots in the kinematogram moving towards a saccadic target, a. Due to the uncertainty in the stimuli, neurons in sensory systems have evolved to transform environmental information, comprising evidence upon which a decision can be made (e.g. saccading to a). The neurons in the middle-temporal area (MT) appear to produce such evidence during the RDMT, given their tuning to a 'preferred' direction of visual motion. If the dots move predominantly in the preferred direction of an MT neuron, it generates inter-spike intervals (ISI) supporting a saccade to a. These ISIs seem randomly sampled from a distribution, f a , with mean, μ a . Otherwise, the ISIs follow another distribution, f b , with mean, μ b , where μ b is larger than μ a and this difference increases with stimulus strength. The accuracy vs motion-strength function of an ideal observer provided with empirical distributions like f a and f b , from a single MT neuron, approximates the subject's psychometric function (at the behavioral level) [1]. The distributions f a and f b are non-negative, positively skewed and have a mode larger than 0 (figure 1A), as is typical for neural events recorded in many brain areas. Here we investigate why this is advantageous for decision-making. As theoretical decision-making units, we produced 5 new instantiations of the multi-hypothesis sequential probability ratio test (MSPRT) [2]. Each unit assumes its stream of input evidence to follow 1 of 5 probability density functions (PDF) whose compatibility with the empirical distribution of ISIs varies (figure 1A). These include the Inverse Gaussian, Lognormal, Gamma, Inverse-Gamma and Exponential PDFs (the latter is the distribution of the inter-event times in the oft-used Poisson process). Under equal and appropriate conditions, we then compared their mean decision sample with that of an MSPRT instantiation that assumes Gaussian inputs proposed in [3] and discussed in general in [4], as exemplified in figure 1B. The mean decision sample is the mean number of observations required by a unit to identify which of N parallel information sources supports saccading to a, with a given accuracy. This decision sample is a model of the 'neural decision time'; the psychophysical reaction time also includes sensory and motor delays. The pattern of our results is explicable using a measure of the discrimination information between f a and f b , i.e. the Kullback-Leibler divergence (KLD). We found that, the mean decision sample decreases with increasing f a to f b KLD and, crucially, this follows a power law (figure 1C). At the behavioral level, Piéron [5] reported the mean reaction time to the presentation of a stimulus (go/no-go decision-making) being shorter for more intense stimuli, and that a power law relates these measures. The universality of Piéron's law indicates that it can inform us of something fundamental about sensorimotor decision-making. Our results suggest that its explanation could lie in the power law relationship between the mean neural decision time and the discrimination information (KLD) among the distributions of sensory evidence.

Figure 1
figure 1

(A) PDFs of interest fitted to ISIs (grey bars) recorded in [1]from the MT during the RDMT. (B) mean decision sample for each MSPRT realisation (accuracy 95% over 1000 trials). (C) the values in (B) vs the fa to fb KLD. The dashed line is a fitted power law. All colour coding as in panel (B).


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This work was sponsored by the Mexican National Science and Technology Council (CONACyT).

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Correspondence to Javier A Caballero.

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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Caballero, J.A., Lepora, N. & Gurney, K.N. Decision-making out of neural events: from discrimination information to psychometric power laws. BMC Neurosci 14 (Suppl 1), P153 (2013).

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