The Speed and Accuracy of a Simple Perceptual Decision: A Mathematical Primer

Shadlen, Michael N.; Hanks, Timothy D.; Churchland, Anne K.; Kiani, Roozbeh; Yang, Tianming

doi:10.7551/mitpress/9780262042383.003.0010

Cited by 81 publications

(113 citation statements)

References 29 publications

(38 reference statements)

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“…Algorithms of this kind have been shown to be able to account for the way in which both the probability of choosing one alternative over the other and the average time required to make a decision vary with changes in the relative value of the two 2 In the neural implementation of such a mechanism for a motion-discrimination task discussed by Shadlen et al (2007), these signals are additional spikes generated either by "left-preferring" or "right-preferring" neurons. 3 In perceptual applications, the log odds are assumed to be a linear function of some objective characteristic of the presented stimulus, such as the "motion strength" in Shadlen et al (2007), rather than a value difference.…”

Section: Accumulation-to-bound Algorithmsmentioning

confidence: 99%

“…4 In the context of motion perception, Shadlen et al (2007) argue that such an algorithm describes neural mechanisms involved in perceptual judgments; both the signals s produced by the sensor and the evolving state variable n of the decoder can be identified with the firing rates of particular populations of neurons in the brain.…”

Section: Accumulation-to-bound Algorithmsmentioning

confidence: 99%

“…3 In perceptual applications, the log odds are assumed to be a linear function of some objective characteristic of the presented stimulus, such as the "motion strength" in Shadlen et al (2007), rather than a value difference.…”

Section: Accumulation-to-bound Algorithmsmentioning

confidence: 99%

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Stochastic Choice: An Optimizing Neuroeconomic Model

Woodford

2014

American Economic Review

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A model is proposed in which stochastic choice results from noise in cognitive processing rather than random variation in preferences. The mental process used to make a choice is nonetheless optimal, subject to a constraint on available information-processing capacity that is partially motivated by neurophysiological evidence. The optimal information-constrained model is found to offer a better fit to experimental data on choice frequencies and reaction times than either a purely mechanical process model of choice (the drift-diffusion model) or an optimizing model with fewer constraints on feasible choice processes (the rational inattention model).Experimental studies often find that choice has an apparently random element (e.g., Hey, 1995;Ballinger and Wilcox, 1997;Cheremukhin, Popova and Tutino, 2011). It is plausible, especially in light of the similarity between the stochasticity of choice behavior and the the stochastic responses observed in perceptual discrimination tasks (e.g., Green and Swets, 1966), to think of this as reflecting noise in the cognitive processing of the choice situation, rather than variation in the subject's genuine preferences. Such a theory, however, makes specific predictions, even of a probabilistic nature, only under a specific hypothesis about the processing errors.Here we offer such a theory, in which the mental process used to make a choice is optimal, in the sense of maximizing expected utility, subject to a constraint on the information-processing capacity of the neural pathways that supply information about the current choice situation. In proposing such an information constraint, the model is in the spirit of Sims' (2010) theory of "rational inattention." However, unlike Sims' theory, the model proposed here imposes additional constraints on the class of choice

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Section: Accumulation-to-bound Algorithmsmentioning

confidence: 99%

Section: Accumulation-to-bound Algorithmsmentioning

confidence: 99%

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Stochastic Choice: An Optimizing Neuroeconomic Model

Woodford

2014

American Economic Review

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“…The simpler version can be seen as a standard signal detection theory task; the more complex one has been analyzed by Shadlen (2001, 2007) as an optimal-stopping problem. This, in turn, is a form of partially observable MDP (POMDP) related to the sequential probability ratio test (SPRT; Ratcliff & Rouder, 1998;Shadlen, Hanks, Churchland, Kiani, & Yang, 2007;Smith & Ratcliff, 2004;Wald, 1947).…”

mentioning

confidence: 99%

Decision theory, reinforcement learning, and the brain

Dayan

Daw

2008

Cognitive, Affective, & Behavioral Neuroscience

498

486

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Decision making is a core competence for animals and humans acting and surviving in environments they only partially comprehend, gaining rewards and punishments for their troubles. Decision-theoretic concepts permeate experiments and computational models in ethology, psychology, and neuroscience. Here, we review permeate experiments and computational models in ethology, psychology, and neuroscience. Here, we review a welln known, coherent Bayesian approach to decision making, showing how it unifies issues in Markovian decision problems, signal detection psychophysics, sequential sampling, and optimal exploration and discuss p paradigmatic psychological and neural examples of each problem. We discuss computational issues concerning what subjects know about their task and how ambitious they are in seeking optimal solutions; we address algorithmic topics concerning model-based and model-free methods for making choices; and we highlight key aspects o t e eu a p e e tat o o dec s o a g. aspects of the neural implementation of decision making.

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“…10). However, the standard DDM predicts identical RTs for correct and incorrect responses (Ratcliff, 1978;Shadlen et al, 2006;Ratcliff and McKoon, 2008). Likewise, the population-code, drift-diffusion model developed above predicts equal correct and incorrect RT distributions (Fig.…”

Section: Speed Versus Accuracy Rt Distribution and Incorrect-trial Rtmentioning

confidence: 99%

A Two-Stage Process Model of Sensory Discrimination: An Alternative to Drift-Diffusion

Sun

Landy

2016

J. Neurosci.

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Discrimination of the direction of motion of a noisy stimulus is an example of sensory discrimination under uncertainty. For stimuli that are extended in time, reaction time is quicker for larger signal values (e.g., discrimination of opposite directions of motion compared with neighboring orientations) and larger signal strength (e.g., stimuli with higher contrast or motion coherence, that is, lower noise). The standard model of neural responses (e.g., in lateral intraparietal cortex) and reaction time for discrimination is drift-diffusion. This model makes two clear predictions.(1) The effects of signal strength and value on reaction time should interact multiplicatively because the diffusion process depends on the signal-to-noise ratio. (2) If the diffusion process is interrupted, as in a cued-response task, the time to decision after the cue should be independent of the strength of accumulated sensory evidence. In two experiments with human participants, we show that neither prediction holds. A simple alternative model is developed that is consistent with the results. In this estimate-then-decide model, evidence is accumulated until estimation precision reaches a threshold value. Then, a decision is made with duration that depends on the signal-to-noise ratio achieved by the first stage.

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The Speed and Accuracy of a Simple Perceptual Decision: A Mathematical Primer

Cited by 81 publications

References 29 publications

Stochastic Choice: An Optimizing Neuroeconomic Model

Stochastic Choice: An Optimizing Neuroeconomic Model

Decision theory, reinforcement learning, and the brain

A Two-Stage Process Model of Sensory Discrimination: An Alternative to Drift-Diffusion

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