Comparing fixed and collapsing boundary versions of the diffusion model

A cross-species framework for investigating perceptual evidence accumulation

Cross-species studies are important for a comprehensive understanding of brain functions. However, direct quantitative comparison of behaviors across species presents a significant challenge. To enable such comparisons in perceptual decision-making, we developed a synchronized evidence accumulation task for rodents and humans, by aligning mechanics, stimuli, and training. Rats, mice and humans readily learned the task and exhibited qualitatively similar performance. Quantitative model comparison revealed that all three species employed an evidence accumulation strategy, but differed in speed, accuracy, and key decision parameters. Human performance prioritized accuracy, whereas rodent performance was limited by internal time-pressure. Rats optimized reward rate, while mice appeared to switch between evidence accumulation and other strategies trial-to-trial. Together, these results reveal striking similarities and species-specific priorities in decision-making. Furthermore, the synchronized behavioral framework we present may facilitate future studies involving cross-species comparisons, such as evaluating the face validity of animal models of neuropsychiatric disorders.

Highlights

Development of a free response evidence accumulation task for rats and miceSynchronized video game allows direct comparisons with humansRat, mouse and human behavior are well fit by the same decision modelsModel parameters reveal species-specific priorities in accumulation strategy.

Attribute latencies causally shape intertemporal decisions

Intertemporal choices - decisions that play out over time - pervade our life. Thus, how people make intertemporal choices is a fundamental question. Here, we investigate the role of attribute latency (the time between when people start to process different attributes) in shaping intertemporal preferences using five experiments with choices between smaller-sooner and larger-later rewards. In the first experiment, we identify attribute latencies using mouse-trajectories and find that they predict individual differences in choices, response times, and changes across time constraints. In the other four experiments we test the causal link from attribute latencies to choice, staggering the display of the attributes. This changes attribute latencies and intertemporal preferences. Displaying the amount information first makes people more patient, while displaying time information first does the opposite. These findings highlight the importance of intra-choice dynamics in shaping intertemporal choices and suggest that manipulating attribute latency may be a useful technique for nudging.

Expressions for Bayesian confidence of drift diffusion observers in fluctuating stimuli tasks

We introduce a new approach to modelling decision confidence, with the aim of enabling computationally cheap predictions while taking into account, and thereby exploiting, trial-by-trial variability in stochastically fluctuating stimuli. Using the framework of the drift diffusion model of decision making, along with time-dependent thresholds and the idea of a Bayesian confidence readout, we derive expressions for the probability distribution over confidence reports. In line with current models of confidence, the derivations allow for the accumulation of "pipeline" evidence that has been received but not processed by the time of response, the effect of drift rate variability, and metacognitive noise. The expressions are valid for stimuli that change over the course of a trial with normally-distributed fluctuations in the evidence they provide. A number of approximations are made to arrive at the final expressions, and we test all approximations via simulation. The derived expressions contain only a small number of standard functions, and require evaluating only once per trial, making trial-by-trial modelling of confidence data in stochastically fluctuating stimuli tasks more feasible. We conclude by using the expressions to gain insight into the confidence of optimal observers, and empirically observed patterns.

"Reliable organisms from unreliable components" revisited: the linear drift, linear infinitesimal variance model of decision making

Diffusion models of decision making, in which successive samples of noisy evidence are accumulated to decision criteria, provide a theoretical solution to von Neumann's (1956) problem of how to increase the reliability of neural computation in the presence of noise. I introduce and evaluate a new neurally-inspired dual diffusion model, the linear drift, linear infinitesimal variance (LDLIV) model, which embodies three features often thought to characterize neural mechanisms of decision making. The accumulating evidence is intrinsically positively-valued, saturates at high intensities, and is accumulated for each alternative separately. I present explicit integral-equation predictions for the response time distribution and choice probabilities for the LDLIV model and compare its performance on two benchmark sets of data to three other models: the standard diffusion model and two dual diffusion model composed of racing Wiener processes, one between absorbing and reflecting boundaries and one with absorbing boundaries only. The LDLIV model and the standard diffusion model performed similarly to one another, although the standard diffusion model is more parsimonious, and both performed appreciably better than the other two dual diffusion models. I argue that accumulation of noisy evidence by a diffusion process and drift rate variability are both expressions of how the cognitive system solves von Neumann's problem, by aggregating noisy representations over time and over elements of a neural population. I also argue that models that do not solve von Neumann's problem do not address the main theoretical question that historically motivated research in this area.

Evidence or Confidence: What Is Really Monitored during a Decision?

Assessing our confidence in the choices we make is important to making adaptive decisions, and it is thus no surprise that we excel in this ability. However, standard models of decision-making, such as the drift-diffusion model (DDM), treat confidence assessment as a post hoc or parallel process that does not directly influence the choice, which depends only on accumulated evidence. Here, we pursue the alternative hypothesis that what is monitored during a decision is an evolving sense of confidence (that the to-be-selected option is the best) rather than raw evidence. Monitoring confidence has the appealing consequence that the decision threshold corresponds to a desired level of confidence for the choice, and that confidence improvements can be traded off against the resources required to secure them. We show that most previous findings on perceptual and value-based decisions traditionally interpreted from an evidence-accumulation perspective can be explained more parsimoniously from our novel confidence-driven perspective. Furthermore, we show that our novel confidence-driven DDM (cDDM) naturally generalizes to decisions involving any number of alternative options - which is notoriously not the case with traditional DDM or related models. Finally, we discuss future empirical evidence that could be useful in adjudicating between these alternatives.

Secondary motor integration as a final arbiter in sensorimotor decision-making

Sensorimotor decision-making is believed to involve a process of accumulating sensory evidence over time. While current theories posit a single accumulation process prior to planning an overt motor response, here, we propose an active role of motor processes in decision formation via a secondary leaky motor accumulation stage. The motor leak adapts the "memory" with which this secondary accumulator reintegrates the primary accumulated sensory evidence, thus adjusting the temporal smoothing in the motor evidence and, correspondingly, the lag between the primary and motor accumulators. We compare this framework against different single accumulator variants using formal model comparison, fitting choice, and response times in a task where human observers made categorical decisions about a noisy sequence of images, under different speed-accuracy trade-off instructions. We show that, rather than boundary adjustments (controlling the amount of evidence accumulated for decision commitment), adjustment of the leak in the secondary motor accumulator provides the better description of behavior across conditions. Importantly, we derive neural correlates of these 2 integration processes from electroencephalography data recorded during the same task and show that these neural correlates adhere to the neural response profiles predicted by the model. This framework thus provides a neurobiologically plausible description of sensorimotor decision-making that captures emerging evidence of the active role of motor processes in choice behavior.

Stimulus-response congruency effects depend on quality of perceptual evidence: A diffusion model account

Individuals often need to make quick decisions based on incomplete or "noisy" information. This requires the coordination of attentional, perceptual, cognitive, and behavioral mechanisms. This poses a challenge for isolating the unique effects of each subprocess from behavioral data, which reflect the summation of all subprocesses combined. Sequential sampling models offer a more detailed examination of behavioral data, enabling us to separate decisional and non-decisional processes at play in a task. Participants were required to identify briefly presented shapes while perceptual (duration, size, location) and response features (location-congruent/-incongruent/-neutral) of the task were manipulated. The diffusion model (Ratcliff, 1978) was used to dissociate decisional and executive processes in the task. In Experiment 1, stimuli were presented for either 20 or 80 ms to the left or right of a central fixation while response keys were positioned horizontally. In Experiment 2, stimulus size was manipulated rather than duration. In Experiment 3, response keys were positioned vertically. Results showed a duration x response mapping interaction. Participants displayed stimulus-response (S-R) congruency biases only on short-duration trials. This effect was observed for both horizontal and vertical response key mappings. Stimulus size affected participant response speed, but did not elicit S-R congruency biases. The present findings show that when perceptual quality of evidence is poor, individuals rely more heavily on spatial-motor mechanisms when making speeded choice decisions. Furthermore, positioning response keys vertically is insufficient to eliminate S-R congruency effects. Diffusion model parameters are presented and implications of the model are discussed.

Temporal order judgment of multisensory stimuli in rat and human

We do not fully understand the resolution at which temporal information is processed by different species. Here we employed a temporal order judgment (TOJ) task in rats and humans to test the temporal precision with which these species can detect the order of presentation of simple stimuli across two modalities of vision and audition. Both species reported the order of audiovisual stimuli when they were presented from a central location at a range of stimulus onset asynchronies (SOA)s. While both species could reliably distinguish the temporal order of stimuli based on their sensory content (i.e., the modality label), rats outperformed humans at short SOAs (less than 100 ms) whereas humans outperformed rats at long SOAs (greater than 100 ms). Moreover, rats produced faster responses compared to humans. The reaction time data further revealed key differences in decision process across the two species: at longer SOAs, reaction times increased in rats but decreased in humans. Finally, drift-diffusion modeling allowed us to isolate the contribution of various parameters including evidence accumulation rates, lapse and bias to the sensory decision. Consistent with the psychophysical findings, the model revealed higher temporal sensitivity and a higher lapse rate in rats compared to humans. These findings suggest that these species applied different strategies for making perceptual decisions in the context of a multimodal TOJ task.

Degenerate boundaries for multiple-alternative decisions

Integration-to-threshold models of two-choice perceptual decision making have guided our understanding of human and animal behavior and neural processing. Although such models seem to extend naturally to multiple-choice decision making, consensus on a normative framework has yet to emerge, and hence the implications of threshold characteristics for multiple choices have only been partially explored. Here we consider sequential Bayesian inference and a conceptualisation of decision making as a particle diffusing in n-dimensions. We show by simulation that, within a parameterised subset of time-independent boundaries, the optimal decision boundaries comprise a degenerate family of nonlinear structures that jointly depend on the state of multiple accumulators and speed-accuracy trade-offs. This degeneracy is contrary to current 2-choice results where there is a single optimal threshold. Such boundaries support both stationary and collapsing thresholds as optimal strategies for decision-making, both of which result from stationary representations of nonlinear boundaries. Our findings point towards a normative theory of multiple-choice decision making, provide a characterisation of optimal decision thresholds under this framework, and inform the debate between stationary and dynamic decision boundaries for optimal decision making.

Evidence integration and decision confidence are modulated by stimulus consistency

Evidence integration is a normative algorithm for choosing between alternatives with noisy evidence, which has been successful in accounting for vast amounts of behavioural and neural data. However, this mechanism has been challenged by non-integration heuristics, and tracking decision boundaries has proven elusive. Here we first show that the decision boundaries can be extracted using a model-free behavioural method termed decision classification boundary, which optimizes choice classification based on the accumulated evidence. Using this method, we provide direct support for evidence integration over non-integration heuristics, show that the decision boundaries collapse across time and identify an integration bias whereby incoming evidence is modulated based on its consistency with preceding information. This consistency bias, which is a form of pre-decision confirmation bias, was supported in four cross-domain experiments, showing that choice accuracy and decision confidence are modulated by stimulus consistency. Strikingly, despite its seeming sub-optimality, the consistency bias fosters performance by enhancing robustness to integration noise.

Modeling evidence accumulation decision processes using integral equations: Urgency-gating and collapsing boundaries

Diffusion models of evidence accumulation have successfully accounted for the distributions of response times and choice probabilities from many experimental tasks, but recently their assumption that evidence is accumulated at a constant rate to constant decision boundaries has been challenged. One model assumes that decision-makers seek to optimize their performance by using decision boundaries that collapse over time. Another model assumes that evidence does not accumulate and is represented by a stationary distribution that is gated by an urgency signal to make a response. We present explicit, integral-equation expressions for the first-passage time distributions of the urgency-gating and collapsing-bounds models and use them to identify conditions under which the models are equivalent. We combine these expressions with a dynamic model of stimulus encoding that allows the effects of perceptual and decisional integration to be distinguished. We compare the resulting models to the standard diffusion model with variability in drift rates on data from three experimental paradigms in which stimulus information was either constant or changed over time. The standard diffusion model was the best model for tasks with constant stimulus information; the models with time-varying urgency or decision bounds performed similarly to the standard diffusion model on tasks with changing stimulus information. We found little support for the claim that evidence does not accumulate and attribute the good performance of the time-varying models on changing-stimulus tasks to their increased flexibility and not to their ability to account for systematic experimental effects. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Magnitude-sensitivity: rethinking decision-making

Magnitude-sensitivity refers to the result that performance in decision-making, across domains and organisms, is affected by the total value of the possible alternatives. This simple result offers a window into fundamental issues in decision-making and has led to a reconsideration of ecological decision-making, prominent computational models of decision-making, and optimal decision-making. Moreover, magnitude-sensitivity has inspired the design of new robotic systems that exploit natural solutions and apply optimal decision-making policies. In this article, we review the key theoretical and empirical results about magnitude-sensitivity and highlight the importance that this phenomenon has for the understanding of decision-making. Furthermore, we discuss open questions and ideas for future research.

Trading accuracy for speed over the course of a decision

Humans and other animals often need to balance the desire to gather sensory information (to make the best choice) with the urgency to act, facing a speed-accuracy tradeoff (SAT). Given the ubiquity of SAT across species, extensive research has been devoted to understanding the computational mechanisms allowing its regulation at different timescales, including from one context to another, and from one decision to another. However, animals must frequently change their SAT on even shorter timescales-that is, over the course of an ongoing decision-and little is known about the mechanisms that allow such rapid adaptations. The present study aimed at addressing this issue. Human subjects performed a decision task with changing evidence. In this task, subjects received rewards for correct answers but incurred penalties for mistakes. An increase or a decrease in penalty occurring halfway through the trial promoted rapid SAT shifts, favoring speeded decisions either in the early or in the late stage of the trial. Importantly, these shifts were associated with stage-specific adjustments in the accuracy criterion exploited for committing to a choice. Those subjects who decreased the most their accuracy criterion at a given decision stage exhibited the highest gain in speed, but also the highest cost in terms of performance accuracy at that time. Altogether, the current findings offer a unique extension of previous work, by suggesting that dynamic cha*nges in accuracy criterion allow the regulation of the SAT within the timescale of a single decision.NEW & NOTEWORTHY Extensive research has been devoted to understanding the mechanisms allowing the regulation of the speed-accuracy tradeoff (SAT) from one context to another and from one decision to another. Here, we show that humans can voluntarily change their SAT on even shorter timescales-that is, over the course of a decision. These rapid SAT shifts are associated with dynamic adjustments in the accuracy criterion exploited for committing to a choice.

Evidence and Urgency Related EEG Signals during Dynamic Decision-Making in Humans

A successful class of models link decision-making to brain signals by assuming that evidence accumulates to a decision threshold. These evidence accumulation models have identified neuronal activity that appears to reflect sensory evidence and decision variables that drive behavior. More recently, an additional evidence-independent and time-variant signal, called urgency, has been hypothesized to accelerate decisions in the face of insufficient evidence. However, most decision-making paradigms tested with fMRI or EEG in humans have not been designed to disentangle evidence accumulation from urgency. Here we use a face-morphing decision-making task in combination with EEG and a hierarchical Bayesian model to identify neural signals related to sensory and decision variables, and to test the urgency-gating model. Forty females and 34 males took part (mean age, 23.4 years). We find that an evoked potential time locked to the decision, the centroparietal positivity, reflects the decision variable from the computational model. We further show that the unfolding of this signal throughout the decision process best reflects the product of sensory evidence and an evidence-independent urgency signal. Urgency varied across subjects, suggesting that it may represent an individual trait. Our results show that it is possible to use EEG to distinguish neural signals related to sensory evidence accumulation, decision variables, and urgency. These mechanisms expose principles of cognitive function in general and may have applications to the study of pathologic decision-making such as in impulse control and addictive disorders.SIGNIFICANCE STATEMENT Perceptual decisions are often described by a class of models that assumes that sensory evidence accumulates gradually over time until a decision threshold is reached. In the present study, we demonstrate that an additional urgency signal impacts how decisions are formed. This endogenous signal encourages one to respond as time elapses. We found that neural decision signals measured by EEG reflect the product of sensory evidence and an evidence-independent urgency signal. A nuanced understanding of human decisions, and the neural mechanisms that support it, can improve decision-making in many situations and potentially ameliorate dysfunction when it has gone awry.

Tracking dynamic adjustments to decision making and performance monitoring processes in conflict tasks

How we exert control over our decision-making has been investigated using conflict tasks, which involve stimuli containing elements that are either congruent or incongruent. In these tasks, participants adapt their decision-making strategies following exposure to incongruent stimuli. According to conflict monitoring accounts, conflicting stimulus features are detected in medial frontal cortex, and the extent of experienced conflict scales with response time (RT) and frontal theta-band activity in the Electroencephalogram (EEG). However, the consequent adjustments to decision processes following response conflict are not well-specified. To characterise these adjustments and their neural implementation we recorded EEG during a modified Flanker task. We traced the time-courses of performance monitoring processes (frontal theta) and multiple processes related to perceptual decision-making. In each trial participants judged which of two overlaid gratings forming a plaid stimulus (termed the S1 target) was of higher contrast. The stimulus was divided into two sections, which each contained higher contrast gratings in either congruent or incongruent directions. Shortly after responding to the S1 target, an additional S2 target was presented, which was always congruent. Our EEG results suggest enhanced sensory evidence representations in visual cortex and reduced evidence accumulation rates for S2 targets following incongruent S1 stimuli. Results of a follow-up behavioural experiment indicated that the accumulation of sensory evidence from the incongruent (i.e. distracting) stimulus element was adjusted following response conflict. Frontal theta amplitudes positively correlated with RT following S1 targets (in line with conflict monitoring accounts). Following S2 targets there was no such correlation, and theta amplitude profiles instead resembled decision evidence accumulation trajectories. Our findings provide novel insights into how cognitive control is implemented following exposure to conflicting information, which is critical for extending conflict monitoring accounts.

Neurophysiology of Human Perceptual Decision-Making

The discovery of neural signals that reflect the dynamics of perceptual decision formation has had a considerable impact. Not only do such signals enable detailed investigations of the neural implementation of the decision-making process but they also can expose key elements of the brain's decision algorithms. For a long time, such signals were only accessible through direct animal brain recordings, and progress in human neuroscience was hampered by the limitations of noninvasive recording techniques. However, recent methodological advances are increasingly enabling the study of human brain signals that finely trace the dynamics of the unfolding decision process. In this review, we highlight how human neurophysiological data are now being leveraged to furnish new insights into the multiple processing levels involved in forming decisions, to inform the construction and evaluation of mathematical models that can explain intra- and interindividual differences, and to examine how key ancillary processes interact with core decision circuits.

An Overcomplete Approach to Fitting Drift-Diffusion Decision Models to Trial-By-Trial Data

Drift-diffusion models or DDMs are becoming a standard in the field of computational neuroscience. They extend models from signal detection theory by proposing a simple mechanistic explanation for the observed relationship between decision outcomes and reaction times (RT). In brief, they assume that decisions are triggered once the accumulated evidence in favor of a particular alternative option has reached a predefined threshold. Fitting a DDM to empirical data then allows one to interpret observed group or condition differences in terms of a change in the underlying model parameters. However, current approaches only yield reliable parameter estimates in specific situations (c.f. fixed drift rates vs drift rates varying over trials). In addition, they become computationally unfeasible when more general DDM variants are considered (e.g., with collapsing bounds). In this note, we propose a fast and efficient approach to parameter estimation that relies on fitting a "self-consistency" equation that RT fulfill under the DDM. This effectively bypasses the computational bottleneck of standard DDM parameter estimation approaches, at the cost of estimating the trial-specific neural noise variables that perturb the underlying evidence accumulation process. For the purpose of behavioral data analysis, these act as nuisance variables and render the model "overcomplete," which is finessed using a variational Bayesian system identification scheme. However, for the purpose of neural data analysis, estimates of neural noise perturbation terms are a desirable (and unique) feature of the approach. Using numerical simulations, we show that this "overcomplete" approach matches the performance of current parameter estimation approaches for simple DDM variants, and outperforms them for more complex DDM variants. Finally, we demonstrate the added-value of the approach, when applied to a recent value-based decision making experiment.

Vision for the blind: visual psychophysics and blinded inference for decision models

Evidence accumulation models like the diffusion model are increasingly used by researchers to identify the contributions of sensory and decisional factors to the speed and accuracy of decision-making. Drift rates, decision criteria, and nondecision times estimated from such models provide meaningful estimates of the quality of evidence in the stimulus, the bias and caution in the decision process, and the duration of nondecision processes. Recently, Dutilh et al. (Psychonomic Bulletin & Review 26, 1051–1069, 2019) carried out a large-scale, blinded validation study of decision models using the random dot motion (RDM) task. They found that the parameters of the diffusion model were generally well recovered, but there was a pervasive failure of selective influence, such that manipulations of evidence quality, decision bias, and caution also affected estimated nondecision times. This failure casts doubt on the psychometric validity of such estimates. Here we argue that the RDM task has unusual perceptual characteristics that may be better described by a model in which drift and diffusion rates increase over time rather than turn on abruptly. We reanalyze the Dutilh et al. data using models with abrupt and continuous-onset drift and diffusion rates and find that the continuous-onset model provides a better overall fit and more meaningful parameter estimates, which accord with the known psychophysical properties of the RDM task. We argue that further selective influence studies that fail to take into account the visual properties of the evidence entering the decision process are likely to be unproductive.

Confluence of Timing and Reward Biases in Perceptual Decision-Making Dynamics

Although the decisions of our daily lives often occur in the context of temporal and reward structures, the impact of such regularities on decision-making strategy is poorly understood. Here, to explore how temporal and reward context modulate strategy, we trained 2 male rhesus monkeys to perform a novel perceptual decision-making task with asymmetric rewards and time-varying evidence reliability. To model the choice and response time patterns, we developed a computational framework for fitting generalized drift-diffusion models, which flexibly accommodate diverse evidence accumulation strategies. We found that a dynamic urgency signal and leaky integration, in combination with two independent forms of reward biases, best capture behavior. We also tested how temporal structure influences urgency by systematically manipulating the temporal structure of sensory evidence, and found that the time course of urgency was affected by temporal context. Overall, our approach identified key components of cognitive mechanisms for incorporating temporal and reward structure into decisions.SIGNIFICANCE STATEMENT In everyday life, decisions are influenced by many factors, including reward structures and stimulus timing. While reward and timing have been characterized in isolation, ecologically valid decision-making involves a multiplicity of factors acting simultaneously. This raises questions about whether the same decision-making strategy is used when these two factors are concurrently manipulated. To address these questions, we trained rhesus monkeys to perform a novel decision-making task with both reward asymmetry and temporal uncertainty. In order to understand their strategy and hint at its neural mechanisms, we used the new generalized drift diffusion modeling framework to model both reward and timing mechanisms. We found two of each reward and timing mechanisms are necessary to explain our data.

Mutual benefits: Combining reinforcement learning with sequential sampling models

Reinforcement learning models of error-driven learning and sequential-sampling models of decision making have provided significant insight into the neural basis of a variety of cognitive processes. Until recently, model-based cognitive neuroscience research using both frameworks has evolved separately and independently. Recent efforts have illustrated the complementary nature of both modelling traditions and showed how they can be integrated into a unified theoretical framework, explaining trial-by-trial dependencies in choice behavior as well as response time distributions. Here, we review a theoretical background of integrating the two classes of models, and review recent empirical efforts towards this goal. We furthermore argue that the integration of both modelling traditions provides mutual benefits for both fields, and highlight promises of this approach for cognitive modelling and model-based cognitive neuroscience.

A theoretical analysis of the reward rate optimality of collapsing decision criteria

A standard assumption of most sequential sampling models is that decision-makers rely on a decision criterion that remains constant throughout the decision process. However, several authors have recently suggested that, in order to maximize reward rates in dynamic environments, decision-makers need to rely on a decision criterion that changes over the course of the decision process. We used dynamic programming and simulation methods to quantify the reward rates obtained by constant and dynamic decision criteria in different environments. We further investigated what influence a decision-maker's uncertainty about the stochastic structure of the environment has on reward rates. Our results show that in most dynamic environments, both types of decision criteria yield similar reward rates, across different levels of uncertainty. This suggests that a static decision criterion might provide a robust default setting.

Integration to boundary in decisions between numerical sequences

Integration-to-boundary is a prominent normative principle used in evidence-based decisions to explain the speed-accuracy trade-off and determine the decision-time. Despite its prominence, however, the decision boundary is not directly observed, but rather is theoretically assumed, and there is still an ongoing debate regarding its form: fixed vs. collapsing. The aim of this study is to show that the integration-to-boundary process extends to decisions between rapid pairs of numerical sequences (2 Hz rate), and to determine the boundary type by directly monitoring the noisy accumulated evidence. In a set of two experiments (supplemented by computational modelling), we demonstrate that integration to a collapsing-boundary takes place in such tasks, ruling out non-integration heuristic strategies. Moreover, we show that participants can adaptively adjust their boundaries in response to reward contingencies. Finally, we discuss the implications to decision optimality and the nature of processes and representations in numerical cognition.

Core body temperature speeds up temporal processing and choice behavior under deadlines

Evidence suggests that human timing ability is compromised by heat. In particular, some studies suggest that increasing body temperature speeds up an internal clock, resulting in faster time perception. However, the consequences of this speed-up for other cognitive processes remain unknown. In the current study, we rigorously tested the speed-up hypothesis by inducing passive hyperthermia through immersion of participants in warm water. In addition, we tested how a change in time perception affects performance in decision making under deadline stress. We found that participants underestimate a prelearned temporal interval when body temperature increases, and that their performance in a two-alternative forced-choice task displays signatures of increased time pressure. These results show not only that timing plays an important role in decision-making, but also that this relationship is mediated by temperature. The consequences for decision-making in job environments that are demanding due to changes in body temperature may be considerable.

Sequential sampling models with variable boundaries and non-normal noise: A comparison of six models

One of the most prominent response-time models in cognitive psychology is the diffusion model, which assumes that decision-making is based on a continuous evidence accumulation described by a Wiener diffusion process. In the present paper, we examine two basic assumptions of standard diffusion model analyses. Firstly, we address the question of whether participants adjust their decision thresholds during the decision process. Secondly, we investigate whether so-called Lévy-flights that allow for random jumps in the decision process account better for experimental data than do diffusion models. Specifically, we compare the fit of six different versions of accumulator models to data from four conditions of a number-letter classification task. The experiment comprised a simple single-stimulus task and a more difficult multiple-stimulus task that were both administered under speed versus accuracy conditions. Across the four experimental conditions, we found little evidence for a collapsing of decision boundaries. However, our results suggest that the Lévy-flight model with heavy-tailed noise distributions (i.e., allowing for jumps in the accumulation process) fits data better than the Wiener diffusion model.

A parameter recovery assessment of time-variant models of decision-making

Evidence accumulation models have been one of the most dominant modeling frameworks used to study rapid decision-making over the past several decades. These models propose that evidence accumulates from the environment until the evidence for one alternative reaches some threshold, typically associated with caution, triggering a response. However, researchers have recently begun to reconsider the fundamental assumptions of how caution varies with time. In the past, it was typically assumed that levels of caution are independent of time. Recent investigations have however suggested the possibility that levels of caution decrease over time and that this strategy provides more efficient performance under certain conditions. Our study provides the first comprehensive assessment of this newer class of models accounting for time-varying caution to determine how robustly their parameters can be estimated. We assess five overall variants of collapsing threshold/urgency signal models based on the diffusion decision model, linear ballistic accumulator model, and urgency gating model frameworks. We find that estimation of parameters, particularly those associated with caution/urgency modulation are most robust for the linearly collapsing threshold diffusion model followed by an urgency-gating model with a leakage process. All other models considered, particularly those with ballistic accumulation or nonlinear thresholds, are unable to recover their own parameters adequately, making their usage in parameter estimation contexts questionable.

Time-varying decision boundaries: insights from optimality analysis

The most widely used account of decision-making proposes that people choose between alternatives by accumulating evidence in favor of each alternative until this evidence reaches a decision boundary. It is frequently assumed that this decision boundary stays constant during a decision, depending on the evidence collected but not on time. Recent experimental and theoretical work has challenged this assumption, showing that constant decision boundaries are, in some circumstances, sub-optimal. We introduce a theoretical model that facilitates identification of the optimal decision boundaries under a wide range of conditions. Time-varying optimal decision boundaries for our model are a result only of uncertainty over the difficulty of each trial and do not require decision deadlines or costs associated with collecting evidence, as assumed by previous authors. Furthermore, the shape of optimal decision boundaries depends on the difficulties of different decisions. When some trials are very difficult, optimal boundaries decrease with time, but for tasks that only include a mixture of easy and medium difficulty trials, the optimal boundaries increase or stay constant. We also show how this simple model can be extended to more complex decision-making tasks such as when people have unequal priors or when they can choose to opt out of decisions. The theoretical model presented here provides an important framework to understand how, why, and whether decision boundaries should change over time in experiments on decision-making.

Single-trial dynamics explain magnitude sensitive decision making

BACKGROUND

Previous research has reported or predicted, on the basis of theoretical and computational work, magnitude sensitive reaction times. Magnitude sensitivity can arise (1) as a function of single-trial dynamics and/or (2) as recent computational work has suggested, while single-trial dynamics may be magnitude insensitive, magnitude sensitivity could arise as a function of overall reward received which in turn affects the speed at which decision boundaries collapse, allowing faster responses as the overall reward received increases.

RESULTS

Here, we review previous theoretical and empirical results and we present new evidence for magnitude sensitivity arising as a function of single-trial dynamics.

CONCLUSIONS

The result of magnitude sensitive reaction times reported is not compatible with single-trial magnitude insensitive models, such as the statistically optimal drift diffusion model.

Biased sequential sampling underlies the effects of time pressure and delay in social decision making

Social decision making involves balancing conflicts between selfishness and pro-sociality. The cognitive processes underlying such decisions are not well understood, with some arguing for a single comparison process, while others argue for dual processes (one intuitive and one deliberative). Here, we propose a way to reconcile these two opposing frameworks. We argue that behavior attributed to intuition can instead be seen as a starting point bias of a sequential sampling model (SSM) process, analogous to a prior in a Bayesian framework. Using mini-dictator games in which subjects make binary decisions about how to allocate money between themselves and another participant, we find that pro-social subjects become more pro-social under time pressure and less pro-social under time delay, while selfish subjects do the opposite. Our findings help reconcile the conflicting results concerning the cognitive processes of social decision making and highlight the importance of modeling the dynamics of the choice process.

It has been proposed that humans make unselfish decisions if constrained to decide quickly, but other research has suggested that time constraint makes us selfish. Here, the authors reconcile these two views showing that pro-social people become more pro-social under time pressure, but selfish subjects do the opposite.

Modeling 2-alternative forced-choice tasks: Accounting for both magnitude and difference effects

We present a model-based analysis of two-alternative forced-choice tasks in which two stimuli are presented side by side and subjects must make a comparative judgment (e.g., which stimulus is brighter). Stimuli can vary on two dimensions, the difference in strength of the two stimuli and the magnitude of each stimulus. Differences between the two stimuli produce typical RT and accuracy effects (i.e., subjects respond more quickly and more accurately when there is a larger difference between the two). However, the overall magnitude of the pair of stimuli also affects RT and accuracy. In the more common two-choice task, a single stimulus is presented and the stimulus varies on only one dimension. In this two-stimulus task, if the standard diffusion decision model is fit to the data with only drift rate (evidence accumulation rate) differing among conditions, the model cannot fit the data. However, if either of one of two variability parameters is allowed to change with stimulus magnitude, the model can fit the data. This results in two models that are extremely constrained with about one tenth of the number of parameters than there are data points while at the same time the models account for accuracy and correct and error RT distributions. While both of these versions of the diffusion model can account for the observed data, the model that allows across-trial variability in drift to vary might be preferred for theoretical reasons. The diffusion model fits are compared to the leaky competing accumulator model which did not perform as well.

Deep Brain Stimulation of the Subthalamic Nucleus Does Not Affect the Decrease of Decision Threshold during the Choice Process When There Is No Conflict, Time Pressure, or Reward

During a decision process, the evidence supporting alternative options is integrated over time, and the choice is made when the accumulated evidence for one of the options reaches a decision threshold. Humans and animals have an ability to control the decision threshold, that is, the amount of evidence that needs to be gathered to commit to a choice, and it has been proposed that the subthalamic nucleus (STN) is important for this control. Recent behavioral and neurophysiological data suggest that, in some circumstances, the decision threshold decreases with time during choice trials, allowing overcoming of indecision during difficult choices. Here we asked whether this within-trial decrease of the decision threshold is mediated by the STN and if it is affected by disrupting information processing in the STN through deep brain stimulation (DBS). We assessed 13 patients with Parkinson disease receiving bilateral STN DBS six or more months after the surgery, 11 age-matched controls, and 12 young healthy controls. All participants completed a series of decision trials, in which the evidence was presented in discrete time points, which allowed more direct estimation of the decision threshold. The participants differed widely in the slope of their decision threshold, ranging from constant threshold within a trial to steeply decreasing. However, the slope of the decision threshold did not depend on whether STN DBS was switched on or off and did not differ between the patients and controls. Furthermore, there was no difference in accuracy and RT between the patients in the on and off stimulation conditions and healthy controls. Previous studies that have reported modulation of the decision threshold by STN DBS or unilateral subthalamotomy in Parkinson disease have involved either fast decision-making under conflict or time pressure or in anticipation of high reward. Our findings suggest that, in the absence of reward, decision conflict, or time pressure for decision-making, the STN does not play a critical role in modulating the within-trial decrease of decision thresholds during the choice process.

Internal and external sources of variability in perceptual decision-making

It is important to identify sources of variability in processing to understand decision-making in perception and cognition. There is a distinction between internal and external variability in processing, and double-pass experiments have been used to estimate their relative contributions. In these and our experiments, exact perceptual stimuli are repeated later in testing, and agreement on the 2 trials is examined to see if it is greater than chance. In recent research in modeling decision processes, some models implement only (internal) variability in the decision process whereas others explicitly represent multiple sources of variability. We describe 5 perceptual double-pass experiments that show greater than chance agreement, which is inconsistent with models that assume internal variability alone. Estimates of total trial-to-trial variability in the evidence accumulation (drift) rate (the decision-relevant stimulus information) were estimated from fits of the standard diffusion decision-making model to the data. The double-pass procedure provided estimates of how much of this total variability was systematic and dependent on the stimulus. These results provide the first behavioral evidence independent of model fits for trial-to-trial variability in drift rate in tasks used in examining perceptual decision-making. (PsycINFO Database Record

Overcoming indecision by changing the decision boundary

The dominant theoretical framework for decision making asserts that people make decisions by integrating noisy evidence to a threshold. It has recently been shown that in many ecologically realistic situations, decreasing the decision boundary maximizes the reward available from decisions. However, empirical support for decreasing boundaries in humans is scant. To investigate this problem, we used an ideal observer model to identify the conditions under which participants should change their decision boundaries with time to maximize reward rate. We conducted 6 expanded-judgment experiments that precisely matched the assumptions of this theoretical model. In this paradigm, participants could sample noisy, binary evidence presented sequentially. Blocks of trials were fixed in duration, and each trial was an independent reward opportunity. Participants therefore had to trade off speed (getting as many rewards as possible) against accuracy (sampling more evidence). Having access to the actual evidence samples experienced by participants enabled us to infer the slope of the decision boundary. We found that participants indeed modulated the slope of the decision boundary in the direction predicted by the ideal observer model, although we also observed systematic deviations from optimality. Participants using suboptimal boundaries do so in a robust manner, so that any error in their boundary setting is relatively inexpensive. The use of a normative model provides insight into what variable(s) human decision makers are trying to optimize. Furthermore, this normative model allowed us to choose diagnostic experiments and in doing so we present clear evidence for time-varying boundaries. (PsycINFO Database Record

Learning to allocate limited time to decisions with different expected outcomes

The goal of this article is to investigate how human participants allocate their limited time to decisions with different properties. We report the results of two behavioral experiments. In each trial of the experiments, the participant must accumulate noisy information to make a decision. The participants received positive and negative rewards for their correct and incorrect decisions, respectively. The stimulus was designed such that decisions based on more accumulated information were more accurate but took longer. Therefore, the total outcome that a participant could achieve during the limited experiments' time depended on her "decision threshold", the amount of information she needed to make a decision. In the first experiment, two types of trials were intermixed randomly: hard and easy. Crucially, the hard trials were associated with smaller positive and negative rewards than the easy trials. A cue presented at the beginning of each trial would indicate the type of the upcoming trial. The optimal strategy was to adopt a small decision threshold for hard trials. The results showed that several of the participants did not learn this simple strategy. We then investigated how the participants adjusted their decision threshold based on the feedback they received in each trial. To this end, we developed and compared 10 computational models for adjusting the decision threshold. The models differ in their assumptions on the shape of the decision thresholds and the way the feedback is used to adjust the decision thresholds. The results of Bayesian model comparison showed that a model with time-varying thresholds whose parameters are updated by a reinforcement learning algorithm is the most likely model. In the second experiment, the cues were not presented. We showed that the optimal strategy is to use a single time-decreasing decision threshold for all trials. The results of the computational modeling showed that the participants did not use this optimal strategy. Instead, they attempted to detect the difficulty of the trial first and then set their decision threshold accordingly.

A martingale analysis of first passage times of time-dependent Wiener diffusion models

Research in psychology and neuroscience has successfully modeled decision making as a process of noisy evidence accumulation to a decision bound. While there are several variants and implementations of this idea, the majority of these models make use of a noisy accumulation between two absorbing boundaries. A common assumption of these models is that decision parameters, e.g., the rate of accumulation (drift rate), remain fixed over the course of a decision, allowing the derivation of analytic formulas for the probabilities of hitting the upper or lower decision threshold, and the mean decision time. There is reason to believe, however, that many types of behavior would be better described by a model in which the parameters were allowed to vary over the course of the decision process. In this paper, we use martingale theory to derive formulas for the mean decision time, hitting probabilities, and first passage time (FPT) densities of a Wiener process with time-varying drift between two time-varying absorbing boundaries. This model was first studied by Ratcliff (1980) in the two-stage form, and here we consider the same model for an arbitrary number of stages (i.e. intervals of time during which parameters are constant). Our calculations enable direct computation of mean decision times and hitting probabilities for the associated multistage process. We also provide a review of how martingale theory may be used to analyze similar models employing Wiener processes by re-deriving some classical results. In concert with a variety of numerical tools already available, the current derivations should encourage mathematical analysis of more complex models of decision making with time-varying evidence.

Global gain modulation generates time-dependent urgency during perceptual choice in humans

Decision-makers must often balance the desire to accumulate information with the costs of protracted deliberation. Optimal, reward-maximizing decision-making can require dynamic adjustment of this speed/accuracy trade-off over the course of a single decision. However, it is unclear whether humans are capable of such time-dependent adjustments. Here, we identify several signatures of time-dependency in human perceptual decision-making and highlight their possible neural source. Behavioural and model-based analyses reveal that subjects respond to deadline-induced speed pressure by lowering their criterion on accumulated perceptual evidence as the deadline approaches. In the brain, this effect is reflected in evidence-independent urgency that pushes decision-related motor preparation signals closer to a fixed threshold. Moreover, we show that global modulation of neural gain, as indexed by task-related fluctuations in pupil diameter, is a plausible biophysical mechanism for the generation of this urgency. These findings establish context-sensitive time-dependency as a critical feature of human decision-making.

Decision-making balances the benefits of additional information with the cost of time, but it is unclear whether humans adjust this balance within individual decisions. Here, authors show that we do make such adjustments to suit contextual demands and suggest that these are driven by modulation of neural gain.