The diffusion decision model allows detailed explanations of behavior in two-choice discrimination tasks. In this article, the model is reviewed to show how it translates behavioral data—accuracy, mean response times, and response time distributions—into components of cognitive processing. Three experiments are used to illustrate experimental manipulations of three components: stimulus difficulty affects the quality of information on which a decision is based; instructions emphasizing either speed or accuracy affect the criterial amounts of information that a subject requires before initiating a response; and the relative proportions of the two stimuli affect biases in drift rate and starting point. The experiments also illustrate the strong constraints that ensure the model is empirically testable and potentially falsifiable. The broad range of applications of the model is also reviewed, including research in the domains of aging and neurophysiology.

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A Bayesian model of continuous speech recognition is presented. It is based on Shortlist (D. Norris, 1994;

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 ≥ 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. KEYWORDS: leaky accumulator, drift-diffusion model, neural network, Hick’s law, multihypothesis sequential test, sequential ratio test.

The authors present a new model of free recall on the basis of M. W. Howard and M. J. Kahana’s (2002a) temporal context model and M. Usher and J. L. McClelland’s (2001) leaky-accumulator decision model. In this model, contextual drift gives rise to both short-term and long-term recency effects, and contextual retrieval gives rise to short-term and long-term contiguity effects. Recall decisions are controlled by a race between competitive leaky accumulators. The model captures the dynamics of immediate, delayed, and continual distractor free recall, demonstrating that dissociations between short- and long-term recency can naturally arise from a model in which an internal contextual state is used as the sole cue for retrieval across time scales.

The authors assume that individuals adapt rationally to a utility function given constraints imposed by their cognitive architecture and the local task environment. This assumption underlies a new approach to modeling and understanding cognition—cognitively bounded rational analysis—that sharpens the predictive acuity of general, integrated theories of cognition and action. Such theories provide the necessary computational means to explain the flexible nature of human behavior but in doing so introduce extreme degrees of freedom in accounting for data. The new approach narrows the space of predicted behaviors through analysis of the payoff achieved by alternative strategies, rather than through fitting strategies and theoretical parameters to data. It extends and complements established approaches, including computational cognitive architectures, rational analysis, optimal motor control, bounded rationality, and signal detection theory. The authors illustrate the approach with a reanalysis of an existing account of psychological refractory period (PRP) dual-task performance and the development and analysis of a new theory of ordered dual-task responses. These analyses yield several novel results, including a new understanding of the role of strategic variation in existing accounts of PRP and the first predictive, quantitative account showing how the details of ordered dual-task phenomena emerge from the rational control of a cognitive system subject to the combined constraints of internal variance, motor interference, and a response selection bottleneck.

1 2 9 2 VOLUME 13 | NUMBER 10 | OCTOBER 2010 nature neurOSCIenCe a r t I C l e S There is a growing consensus in behavioral neuroscience that the brain makes simple choices by first assigning a value to all of the options under consideration and then comparing them Although many popular models of value-based choice implicitly assume that the comparison process involves a trivial instantaneous maximization problem 4,5 , casual observation suggests that the underlying processes are more sophisticated and that visual fixations are likely to be involved. Consider, for example, a typical buyer at the grocery store choosing between two snacks. Instead of approaching the shelf and immediately selecting his preferred option, the individual's gaze shifts repeatedly between the items until one of them is eventually selected. We propose a model of how simple value-based binary choices are made and of the role of visual fixations in the comparison of values. The model makes stark qualitative and quantitative predictions about the relationship between fixation patterns and choices, which we test using eye-tracking There are two key differences between our work and the previous studies on perceptual discrimination. First, in both tasks subjects must determine the value of two potential responses, but in perceptual discrimination tasks subjects typically see a single stochastic stimulus, whereas in our task subjects see two non-stochastic pictures of food items. Second, fixations are not involved in the standard perceptual discrimination task because subjects maintain central fixation at all times, whereas here the fixations are crucial for the decisions. The key idea of our model is that fixations affect the DDM value comparison process by introducing a temporary drift bias toward the fixated item. This drift bias in turn leads to a choice bias for items that are fixated on more. RESULTS Computational model Following the literature on DDMs, our model assumes that the brain computes a relative decision value (RDV) that evolves over time as a Markov Gaussian process until a choice is made The key difference between our model and the standard drift diffusion model is that in our model the slope with which the RDV signal evolves at any particular instant depends on the fixation location. In particular, the slope is proportional to the weighted difference between the values of the fixated and unfixated items. The weight discounts the value of the unfixated item relative to the fixated one. When the subject is looking at the left item the RDV changes according to V t = V t−1 + d(r left − θr right ) +  t , and when he looks at the right item, it changes according to V t = V t−1 + d(r right − θr left ) +  t , where V t is the value of the RDV at time t, r left and r right denote the values of the two options, d is a constant that controls the speed of integration (in units of ms −1 ), θ between 0 and 1 is a parameter that reflects the bias toward the fixated option, and  t is white Gaussian noise with variance σ 2 (randomly sampled once every millisecond). Most organisms facing a choice between multiple stimuli will look repeatedly at them, presumably implementing a comparison process between the items' values. Little is known about the nature of the comparison process in value-based decision-making or about the role of visual fixations in this process. We created a computational model of value-based binary choice in which fixations guide the comparison process and tested it on humans using eye-tracking. We found that the model can quantitatively explain complex relationships between fixation patterns and choices, as well as several fixation-driven decision biases.

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The concept of error detection plays a central role in theories of executive control. In this article, the authors present a mechanism that can rapidly detect errors in speeded response time tasks. This error monitor assigns values to the output of cognitive processes involved in stimulus categorization and response generation and detects errors by identifying states of the system associated with negative value. The mechanism is formalized in a computational model based on a recent theoretical framework for understanding error processing in humans (C. B. Holroyd & M. G. H. Coles, 2002). The model is used to simulate behavioral and event-related brain potential data in a speeded response time task, and the results of the simulation are compared with empirical data. Frontal parts of the brain, including the prefrontal cortex (Luria, 1973; Stuss & Knight, 2002), the anterior cingulate cortex (Devinsky, Morrell, & Vogt, 1995; Posner & DiGirolamo, 1998), and their connections with the basal ganglia (L. L. Brown, Schneider, & Lidsky, 1997; Cummings, 1993), are thought to compose an executive system for cognitive control. The functions of this system are thought to include setting high-level goals, directing other

We study the synthesis of neural coding, selective attention and perceptual decision making. A hierarchical neural architecture is proposed, which implements Bayesian integration of noisy sensory input and topdown attentional priors, leading to sound perceptual discrimination. The model offers an explicit explanation for the experimentally observed modulation that prior information in one stimulus feature (location) can have on an independent feature (orientation). The network’s intermediate levels of representation instantiate known physiological properties of visual cortical neurons. The model also illustrates a possible reconciliation of cortical and neuromodulatory representations of uncertainty. 1