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Zbl 1139.91028
McMillen, Tyler; Holmes, Philip
The dynamics of choice among multiple alternatives. (English)
[J] J. Math. Psychol. 50, No. 1, 30-57 (2006). ISSN 0022-2496

Summary: We consider neurally based models for decision-making in the presence of noisy incoming data. The two-alternative forced-choice task has been extensively studied, and in that case it is known that mutually inhibited leaky integrators in which leakage and inhibition balance can closely approximate a drift-diffusion process that is the continuum limit of the optimal sequential probability ratio test (SPRT). Here we study the performance of neural integrators in $n\geq 2$ alternative choice tasks and relate them to a multihypothesis sequential probability ratio test (MSPRT) that is asymptotically optimal in the limit of vanishing error rates. While a simple race model can implement this `max-vs-next' MSPRT, it requires an additional computational layer, while absolute threshold crossing tests do not require such a layer. Race models with absolute thresholds perform relatively poorly, but we show that a balanced leaky accumulator model with an absolute crossing criterion can approximate a `max-vs-ave' test that is intermediate in performance between the absolute and max-vs-next tests. We consider free and fixed time response protocols, and show that the resulting mean reaction times under the former and decision times for fixed accuracy under the latter obey versions of Hick's law in the low error rate range, and we interpret this in terms of information gained. Specifically, we derive relationships of the forms $\log(n-1)$, $\log(n)$, or $\log(n+1)$ depending on error rates, signal-to-noise ratio, and the test itself. We focus on linearized models, but also consider nonlinear effects of neural activities (firing rates) that are bounded below and show how they modify Hick's law.

MSC 2000:: *91E45 Measurement and performance
62L10 Sequential statistical analysis
62M45 Neural nets and related approaches
92B20 General theory of neural networks

Keywords: Leaky accumulator; drift-diffusion model; neural network; Hick's law; multi-hypothesis sequential test; sequential ratio test

Cited in: Zbl 1197.94091

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