Decision confidence and uncertainty in diffusion models with partially correlated neuronal integrators

Joint modeling of choices and reaction times based on Bayesian contextual behavioral control

In cognitive neuroscience and psychology, reaction times are an important behavioral measure. However, in instrumental learning and goal-directed decision making experiments, findings often rely only on choice probabilities from a value-based model, instead of reaction times. Recent advancements have shown that it is possible to connect value-based decision models with reaction time models. However, typically these models do not provide an integrated account of both value-based choices and reaction times, but simply link two types of models. Here, we propose a novel integrative joint model of both choices and reaction times by combining a computational account of Bayesian sequential decision making with a sampling procedure. This allows us to describe how internal uncertainty in the planning process shapes reaction time distributions. Specifically, we use a recent context-specific Bayesian forward planning model which we extend by a Markov chain Monte Carlo (MCMC) sampler to obtain both choices and reaction times. As we will show this makes the sampler an integral part of the decision making process and enables us to reproduce, using simulations, well-known experimental findings in value based-decision making as well as classical inhibition and switching tasks. Specifically, we use the proposed model to explain both choice behavior and reaction times in instrumental learning and automatized behavior, in the Eriksen flanker task and in task switching. These findings show that the proposed joint behavioral model may describe common underlying processes in these different decision making paradigms.

A low-dimensional approximation of optimal confidence

Human decision making is accompanied by a sense of confidence. According to Bayesian decision theory, confidence reflects the learned probability of making a correct response, given available data (e.g., accumulated stimulus evidence and response time). Although optimal, independently learning these probabilities for all possible data combinations is computationally intractable. Here, we describe a novel model of confidence implementing a low-dimensional approximation of this optimal yet intractable solution. This model allows efficient estimation of confidence, while at the same time accounting for idiosyncrasies, different kinds of biases and deviation from the optimal probability correct. Our model dissociates confidence biases resulting from the estimate of the reliability of evidence by individuals (captured by parameter α), from confidence biases resulting from general stimulus independent under and overconfidence (captured by parameter β). We provide empirical evidence that this model accurately fits both choice data (accuracy, response time) and trial-by-trial confidence ratings simultaneously. Finally, we test and empirically validate two novel predictions of the model, namely that 1) changes in confidence can be independent of performance and 2) selectively manipulating each parameter of our model leads to distinct patterns of confidence judgments. As a tractable and flexible account of the computation of confidence, our model offers a clear framework to interpret and further resolve different forms of confidence biases.

Manipulating Prior Beliefs Causally Induces Under- and Overconfidence

Humans differ vastly in the confidence they assign to decisions. Although such under- and overconfidence relate to fundamental life outcomes, a computational account specifying the underlying mechanisms is currently lacking. We propose that prior beliefs in the ability to perform a task explain confidence differences across participants and tasks, despite similar performance. In two perceptual decision-making experiments, we show that manipulating prior beliefs about performance during training causally influences confidence in healthy adults (N = 50 each; Experiment 1: 8 men, one nonbinary; Experiment 2: 5 men) during a test phase, despite unaffected objective performance. This is true when prior beliefs are induced via manipulated comparative feedback and via manipulated training-phase difficulty. Our results were accounted for within an accumulation-to-bound model, explicitly modeling prior beliefs on the basis of earlier task exposure. Decision confidence is quantified as the probability of being correct conditional on prior beliefs, causing under- or overconfidence. We provide a fundamental mechanistic insight into the computations underlying under- and overconfidence.

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.

Judging the difficulty of perceptual decisions

Deciding how difficult it is going to be to perform a task allows us to choose between tasks, allocate appropriate resources, and predict future performance. To be useful for planning, difficulty judgments should not require completion of the task. Here, we examine the processes underlying difficulty judgments in a perceptual decision-making task. Participants viewed two patches of dynamic random dots, which were colored blue or yellow stochastically on each appearance. Stimulus coherence (the probability, pblue, of a dot being blue) varied across trials and patches thus establishing difficulty, |pblue -0.5|. Participants were asked to indicate for which patch it would be easier to decide the dominant color. Accuracy in difficulty decisions improved with the difference in the stimulus difficulties, whereas the reaction times were not determined solely by this quantity. For example, when the patches shared the same difficulty, reaction times were shorter for easier stimuli. A comparison of several models of difficulty judgment suggested that participants compare the absolute accumulated evidence from each stimulus and terminate their decision when they differed by a set amount. The model predicts that when the dominant color of each stimulus is known, reaction times should depend only on the difference in difficulty, which we confirm empirically. We also show that this model is preferred to one that compares the confidence one would have in making each decision. The results extend evidence accumulation models, used to explain choice, reaction time, and confidence to prospective judgments of difficulty.

Beyond simple laboratory studies: Developing sophisticated models to study rich behavior

Psychology and neuroscience are concerned with the study of behavior, of internal cognitive processes, and their neural foundations. However, most laboratory studies use constrained experimental settings that greatly limit the range of behaviors that can be expressed. While focusing on restricted settings ensures methodological control, it risks impoverishing the object of study: by restricting behavior, we might miss key aspects of cognitive and neural functions. In this article, we argue that psychology and neuroscience should increasingly adopt innovative experimental designs, measurement methods, analysis techniques and sophisticated computational models to probe rich, ecologically valid forms of behavior, including social behavior. We discuss the challenges of studying rich forms of behavior as well as the novel opportunities offered by state-of-the-art methodologies and new sensing technologies, and we highlight the importance of developing sophisticated formal models. We exemplify our arguments by reviewing some recent streams of research in psychology, neuroscience and other fields (e.g., sports analytics, ethology and robotics) that have addressed rich forms of behavior in a model-based manner. We hope that these "success cases" will encourage psychologists and neuroscientists to extend their toolbox of techniques with sophisticated behavioral models - and to use them to study rich forms of behavior as well as the cognitive and neural processes that they engage.

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.

Modality independent or modality specific? Common computations underlie confidence judgements in visual and auditory decisions

The mechanisms that enable humans to evaluate their confidence across a range of different decisions remain poorly understood. To bridge this gap in understanding, we used computational modelling to investigate the processes that underlie confidence judgements for perceptual decisions and the extent to which these computations are the same in the visual and auditory modalities. Participants completed two versions of a categorisation task with visual or auditory stimuli and made confidence judgements about their category decisions. In each modality, we varied both evidence strength, (i.e., the strength of the evidence for a particular category) and sensory uncertainty (i.e., the intensity of the sensory signal). We evaluated several classes of computational models which formalise the mapping of evidence strength and sensory uncertainty to confidence in different ways: 1) unscaled evidence strength models, 2) scaled evidence strength models, and 3) Bayesian models. Our model comparison results showed that across tasks and modalities, participants take evidence strength and sensory uncertainty into account in a way that is consistent with the scaled evidence strength class. Notably, the Bayesian class provided a relatively poor account of the data across modalities, particularly in the more complex categorisation task. Our findings suggest that a common process is used for evaluating confidence in perceptual decisions across domains, but that the parameter settings governing the process are tuned differently in each modality. Overall, our results highlight the impact of sensory uncertainty on confidence and the unity of metacognitive processing across sensory modalities.

Judging the difficulty of perceptual decisions

Deciding how difficult it is going to be to perform a task allows us to choose between tasks, allocate appropriate resources, and predict future performance. To be useful for planning, difficulty judgments should not require completion of the task. Here we examine the processes underlying difficulty judgments in a perceptual decision making task. Participants viewed two patches of dynamic random dots, which were colored blue or yellow stochastically on each appearance. Stimulus coherence (the probability, p blue , of a dot being blue) varied across trials and patches thus establishing difficulty, p blue - 0.5 . Participants were asked to indicate for which patch it would be easier to decide the dominant color. Accuracy in difficulty decisions improved with the difference in the stimulus difficulties, whereas the reaction times were not determined solely by this quantity. For example, when the patches shared the same difficulty, reaction times were shorter for easier stimuli. A comparison of several models of difficulty judgment suggested that participants compare the absolute accumulated evidence from each stimulus and terminate their decision when they differed by a set amount. The model predicts that when the dominant color of each stimulus is known, reaction times should depend only on the difference in difficulty, which we confirm empirically. We also show that this model is preferred to one that compares the confidence one would have in making each decision. The results extend evidence accumulation models, used to explain choice, reaction time and confidence to prospective judgments of difficulty.

Mood and implicit confidence independently fluctuate at different time scales

Mood is an important ingredient of decision-making. Human beings are immersed into a sea of ​​emotions where episodes of high mood alternate with episodes of low mood. While changes in mood are well characterized, little is known about how these fluctuations interact with metacognition, and in particular with confidence about our decisions. We evaluated how implicit measurements of confidence are related with mood states of human participants through two online longitudinal experiments involving mood self-reports and visual discrimination decision-making tasks. Implicit confidence was assessed on each session by monitoring the proportion of opt-out trials when an opt-out option was available, as well as the median reaction time on standard correct trials as a secondary proxy of confidence. We first report a strong coupling between mood, stress, food enjoyment, and quality of sleep reported by participants in the same session. Second, we confirmed that the proportion of opt-out responses as well as reaction times in non-opt-out trials provided reliable indices of confidence in each session. We introduce a normative measure of overconfidence based on the pattern of opt-out selection and the signal-detection-theory framework. Finally and crucially, we found that mood, sleep quality, food enjoyment, and stress level are not consistently coupled with these implicit confidence markers, but rather they fluctuate at different time scales: mood-related states display faster fluctuations (over one day or half-a-day) than confidence level (two-and-a-half days). Therefore, our findings suggest that spontaneous fluctuations of mood and confidence in decision making are independent in the healthy adult population.

Dynamic influences on static measures of metacognition

Humans differ in their capability to judge choice accuracy via confidence judgments. Popular signal detection theoretic measures of metacognition, such as M-ratio, do not consider the dynamics of decision making. This can be problematic if response caution is shifted to alter the tradeoff between speed and accuracy. Such shifts could induce unaccounted-for sources of variation in the assessment of metacognition. Instead, evidence accumulation frameworks consider decision making, including the computation of confidence, as a dynamic process unfolding over time. Using simulations, we show a relation between response caution and M-ratio. We then show the same pattern in human participants explicitly instructed to focus on speed or accuracy. Finally, this association between M-ratio and response caution is also present across four datasets without any reference towards speed. In contrast, when data are analyzed with a dynamic measure of metacognition, v-ratio, there is no effect of speed-accuracy tradeoff.

Optimal Allocation of Finite Sampling Capacity in Accumulator Models of Multialternative Decision Making

When facing many options, we narrow down our focus to very few of them. Although behaviors like this can be a sign of heuristics, they can actually be optimal under limited cognitive resources. Here, we study the problem of how to optimally allocate limited sampling time to multiple options, modeled as accumulators of noisy evidence, to determine the most profitable one. We show that the effective sampling capacity of an agent increases with both available time and the discriminability of the options, and optimal policies undergo a sharp transition as a function of it. For small capacity, it is best to allocate time evenly to exactly five options and to ignore all the others, regardless of the prior distribution of rewards. For large capacities, the optimal number of sampled accumulators grows sublinearly, closely following a power law as a function of capacity for a wide variety of priors. We find that allocating equal times to the sampled accumulators is better than using uneven time allocations. Our work highlights that multialternative decisions are endowed with breadth–depth tradeoffs, demonstrates how their optimal solutions depend on the amount of limited resources and the variability of the environment, and shows that narrowing down to a handful of options is always optimal for small capacities.

Bayesian inference with incomplete knowledge explains perceptual confidence and its deviations from accuracy

In perceptual decisions, subjects infer hidden states of the environment based on noisy sensory information. Here we show that both choice and its associated confidence are explained by a Bayesian framework based on partially observable Markov decision processes (POMDPs). We test our model on monkeys performing a direction-discrimination task with post-decision wagering, demonstrating that the model explains objective accuracy and predicts subjective confidence. Further, we show that the model replicates well-known discrepancies of confidence and accuracy, including the hard-easy effect, opposing effects of stimulus variability on confidence and accuracy, dependence of confidence ratings on simultaneous or sequential reports of choice and confidence, apparent difference between choice and confidence sensitivity, and seemingly disproportionate influence of choice-congruent evidence on confidence. These effects may not be signatures of sub-optimal inference or discrepant computational processes for choice and confidence. Rather, they arise in Bayesian inference with incomplete knowledge of the environment.

Separable neural signatures of confidence during perceptual decisions

Perceptual confidence is an evaluation of the validity of perceptual decisions. While there is behavioural evidence that confidence evaluation differs from perceptual decision-making, disentangling these two processes remains a challenge at the neural level. Here, we examined the electrical brain activity of human participants in a protracted perceptual decision-making task where observers tend to commit to perceptual decisions early whilst continuing to monitor sensory evidence for evaluating confidence. Premature decision commitments were revealed by patterns of spectral power overlying motor cortex, followed by an attenuation of the neural representation of perceptual decision evidence. A distinct neural representation was associated with the computation of confidence, with sources localised in the superior parietal and orbitofrontal cortices. In agreement with a dissociation between perception and confidence, these neural resources were recruited even after observers committed to their perceptual decisions, and thus delineate an integral neural circuit for evaluating perceptual decision confidence.

Fixation patterns in simple choice reflect optimal information sampling

Simple choices (e.g., eating an apple vs. an orange) are made by integrating noisy evidence that is sampled over time and influenced by visual attention; as a result, fluctuations in visual attention can affect choices. But what determines what is fixated and when? To address this question, we model the decision process for simple choice as an information sampling problem, and approximate the optimal sampling policy. We find that it is optimal to sample from options whose value estimates are both high and uncertain. Furthermore, the optimal policy provides a reasonable account of fixations and choices in binary and trinary simple choice, as well as the differences between the two cases. Overall, the results show that the fixation process during simple choice is influenced dynamically by the value estimates computed during the decision process, in a manner consistent with optimal information sampling.

Heterogeneity Improves Speed and Accuracy in Social Networks

How does temporally structured private and social information shape collective decisions? To address this question we consider a network of rational agents who independently accumulate private evidence that triggers a decision upon reaching a threshold. When seen by the whole network, the first agent's choice initiates a wave of new decisions; later decisions have less impact. In heterogeneous networks, first decisions are made quickly by impulsive individuals who need little evidence to make a choice but, even when wrong, can reveal the correct options to nearly everyone else. We conclude that groups comprised of diverse individuals can make more efficient decisions than homogenous ones.

Second Guessing in Perceptual Decision-Making

Human subjects of both sexes were asked to make a perceptual decision between multiple directions of visual motion. In addition to reporting a primary choice, they also had to report a second guess, indicating which of the remaining options they would rather bet on, assuming that they got their primary choice wrong. The second guess was clearly informed by the amounts of sensory evidence that were provided for the different options. A single computational integration-to-threshold model, based on the assumption that the second guess is determined by the rank ordering of accumulated evidence at or shortly after the time of the decision, was able to explain the distribution of primary choices, associated response times, and the distribution of second guesses. This suggests that the decision-maker has access to how well supported unchosen options are by the sensory evidence.SIGNIFICANCE STATEMENT Perceptual decisions require conversion of sensory evidence into a discrete choice. Computational models based on the accumulation of evidence to a decision threshold can explain the distribution of choices and associated decision times. Subjects are also able to report the level of confidence in their decision. Here we show that, when making decisions between more than two alternatives, the decision-maker can even report a second guess that is clearly informed by the sensory evidence. These second guesses show a distribution that is consistent with subjects having access to how much sensory evidence was accumulated for the unchosen options. The decision-maker therefore has knowledge about the outcome of the decision process that goes beyond just the choice and an associated confidence.

Nonlinear neural network dynamics accounts for human confidence in a sequence of perceptual decisions

Electrophysiological recordings during perceptual decision tasks in monkeys suggest that the degree of confidence in a decision is based on a simple neural signal produced by the neural decision process. Attractor neural networks provide an appropriate biophysical modeling framework, and account for the experimental results very well. However, it remains unclear whether attractor neural networks can account for confidence reports in humans. We present the results from an experiment in which participants are asked to perform an orientation discrimination task, followed by a confidence judgment. Here we show that an attractor neural network model quantitatively reproduces, for each participant, the relations between accuracy, response times and confidence. We show that the attractor neural network also accounts for confidence-specific sequential effects observed in the experiment (participants are faster on trials following high confidence trials). Remarkably, this is obtained as an inevitable outcome of the network dynamics, without any feedback specific to the previous decision (that would result in, e.g., a change in the model parameters before the onset of the next trial). Our results thus suggest that a metacognitive process such as confidence in one's decision is linked to the intrinsically nonlinear dynamics of the decision-making neural network.

Learning optimal decisions with confidence

Diffusion decision models (DDMs) are immensely successful models for decision making under uncertainty and time pressure. In the context of perceptual decision making, these models typically start with two input units, organized in a neuron-antineuron pair. In contrast, in the brain, sensory inputs are encoded through the activity of large neuronal populations. Moreover, while DDMs are wired by hand, the nervous system must learn the weights of the network through trial and error. There is currently no normative theory of learning in DDMs and therefore no theory of how decision makers could learn to make optimal decisions in this context. Here, we derive such a rule for learning a near-optimal linear combination of DDM inputs based on trial-by-trial feedback. The rule is Bayesian in the sense that it learns not only the mean of the weights but also the uncertainty around this mean in the form of a covariance matrix. In this rule, the rate of learning is proportional (respectively, inversely proportional) to confidence for incorrect (respectively, correct) decisions. Furthermore, we show that, in volatile environments, the rule predicts a bias toward repeating the same choice after correct decisions, with a bias strength that is modulated by the previous choice's difficulty. Finally, we extend our learning rule to cases for which one of the choices is more likely a priori, which provides insights into how such biases modulate the mechanisms leading to optimal decisions in diffusion models.

Human confidence judgments reflect reliability-based hierarchical integration of contextual information

Our immediate observations must be supplemented with contextual information to resolve ambiguities. However, the context is often ambiguous too, and thus it should be inferred itself to guide behavior. Here, we introduce a novel hierarchical task (airplane task) in which participants should infer a higher-level, contextual variable to inform probabilistic inference about a hidden dependent variable at a lower level. By controlling the reliability of past sensory evidence through varying the sample size of the observations, we find that humans estimate the reliability of the context and combine it with current sensory uncertainty to inform their confidence reports. Behavior closely follows inference by probabilistic message passing between latent variables across hierarchical state representations. Commonly reported inferential fallacies, such as sample size insensitivity, are not present, and neither did participants appear to rely on simple heuristics. Our results reveal uncertainty-sensitive integration of information at different hierarchical levels and temporal scales.

Because our immediate observations are often ambiguous, we must use the context (prior beliefs) to guide inference, but the context may also be uncertain. Here, the authors show that humans can accurately estimate the reliability of the context and combine it with sensory uncertainty to form their decisions and estimate confidence.

Family of closed-form solutions for two-dimensional correlated diffusion processes

Diffusion processes with boundaries are models of transport phenomena with wide applicability across many fields. These processes are described by their probability density functions (PDFs), which often obey Fokker-Planck equations (FPEs). While obtaining analytical solutions is often possible in the absence of boundaries, obtaining closed-form solutions to the FPE is more challenging once absorbing boundaries are present. As a result, analyses of these processes have largely relied on approximations or direct simulations. In this paper, we studied two-dimensional, time-homogeneous, spatially correlated diffusion with linear, axis-aligned, absorbing boundaries. Our main result is the explicit construction of a full family of closed-form solutions for their PDFs using the method of images. We found that such solutions can be built if and only if the correlation coefficient ρ between the two diffusing processes takes one of a numerable set of values. Using a geometric argument, we derived the complete set of ρ's where such solutions can be found. Solvable ρ's are given by ρ=-cos(π/k), where k∈Z^{+}∪{+∞}. Solutions were validated in simulations. Qualitative behaviors of the process appear to vary smoothly over ρ, allowing extrapolation from our solutions to cases with unsolvable ρ's.

Confidence Representation of Perceptual Decision by EEG and Eye Data in a Random Dot Motion Task

The Confidence of a decision could be considered as the internal estimate of decision accuracy. This variable has been studied extensively by different types of recording data such as behavioral, electroencephalography (EEG), eye and electrophysiology data. Although the value of the reported confidence is considered as one of the most important parameters in decision making, the confidence reporting phase might be considered as a restrictive element in investigating the decision process. Thus, decision confidence should be extracted by means of other provided types of information. Here, we proposed eight confidence related properties in EEG and eye data which are significantly descriptive of the defined confidence levels in a random dot motion (RDM) task. As a matter of fact, our proposed EEG and eye data properties are capable of recognizing more than nine distinct levels of confidence. Among our proposed features, the latency of the pupil maximum diameter through the stimulus presentation was established to be the most associated one to the confidence levels. Through the time-dependent analysis of these features, we recognized the time interval of 500-600 ms after the stimulus onset as an important time in correlating features to the confidence levels.

Confidence modulates exploration and exploitation in value-based learning

Uncertainty is ubiquitous in cognitive processing. In this study, we aim to investigate the ability agents possess to track and report the noise inherent in their mental operations, often in the form of confidence judgments. Here, we argue that humans can use uncertainty inherent in their representations of value beliefs to arbitrate between exploration and exploitation. Such uncertainty is reflected in explicit confidence judgments. Using a novel variant of a multi-armed bandit paradigm, we studied how beliefs were formed and how uncertainty in the encoding of these value beliefs (belief confidence) evolved over time. We found that people used uncertainty to arbitrate between exploration and exploitation, reflected in a higher tendency toward exploration when their confidence in their value representations was low. We furthermore found that value uncertainty can be linked to frameworks of metacognition in decision making in two ways. First, belief confidence drives decision confidence, i.e. people's evaluation of their own choices. Second, individuals with higher metacognitive insight into their choices were also better at tracing the uncertainty in their environment. Together, these findings argue that such uncertainty representations play a key role in the context of cognitive control.

Modeling Responses and Response Times in Rating Scales With the Linear Ballistic Accumulator

Abstract. In this article, a new model is proposed for the responses and the response times in attitudinal or personality inventories with graded response format. The model is based on the lognormal race model ( Heathcote & Love, 2012 ) and assumes two accumulators that aggregate evidence in favor of and against the statement made by an item of an inventory. The accumulator that first reaches a response threshold determines the direction of the response (agreement/disagreement). The strength of the response, which is indicated by the choice of a graded response option, is a function of the difference between the two accumulators when responding. By relating the accumulators to latent traits, the model can be embedded into a latent trait model that accounts for individual differences. The model can be fit to data with marginal maximum likelihood estimation. A test of model fit is described, and it is shown how the model can be used for attitudinal and personality assessment. Finally, the application of the model is demonstrated with a real dataset.

Instance-based generalization for human judgments about uncertainty

While previous studies have shown that human behavior adjusts in response to uncertainty, it is still not well understood how uncertainty is estimated and represented. As probability distributions are high dimensional objects, only constrained families of distributions with a low number of parameters can be specified from finite data. However, it is unknown what the structural assumptions are that the brain uses to estimate them. We introduce a novel paradigm that requires human participants of either sex to explicitly estimate the dispersion of a distribution over future observations. Judgments are based on a very small sample from a centered, normally distributed random variable that was suggested by the framing of the task. This probability density estimation task could optimally be solved by inferring the dispersion parameter of a normal distribution. We find that although behavior closely tracks uncertainty on a trial-by-trial basis and resists an explanation with simple heuristics, it is hardly consistent with parametric inference of a normal distribution. Despite the transparency of the simple generating process, participants estimate a distribution biased towards the observed instances while still strongly generalizing beyond the sample. The inferred internal distributions can be well approximated by a nonparametric mixture of spatially extended basis distributions. Thus, our results suggest that fluctuations have an excessive effect on human uncertainty judgments because of representations that can adapt overly flexibly to the sample. This might be of greater utility in more general conditions in structurally uncertain environments.

Are three heavy tropical storms this year compelling evidence for climate change? A suspicious clustering of events may reflect a real change of the environment or might be due to random fluctuations because our world is uncertain. To generalize well, we should build a probability distribution over our observations defined in terms of latent causes. If data is scarce we are forced to make strong assumptions about the shape of the distribution ideally incorporating our prior knowledge. In our task, human behavior is consistent with probabilistic inference but reveals a tendency to generalize based on observed instances enhancing the effect of random patterns on behavioral judgments. The decreased reliance on available constraints through prior knowledge corresponds to a dominance of bottom-up sensory information. Maintaining a balance with expectation-driven top-down information is crucial for proper generalization. Our work provides evidence for the necessity to include graded instance-based generalization into the mathematical formulation of cognitive models. The investigation of the determinants and neural substrates of this inferential bias is expected to give insights into the richness but also fallibility of human inferences.

What can neuronal populations tell us about cognition?

Nowadays, it is possible to record the activity of hundreds of cells at the same time in behaving animals. However, these data are often treated and analyzed as if they consisted of many independently recorded neurons. How can neuronal populations be uniquely used to learn about cognition? We describe recent work that shows that populations of simultaneously recorded neurons are fundamental to understand the basis of decision-making, including processes such as ongoing deliberations and decision confidence, which generally fall outside the reach of single-cell analysis. Thus, neuronal population data allow addressing novel questions, but they also come with so far unsolved challenges.

Self-evaluation of decision-making: A general Bayesian framework for metacognitive computation

People are often aware of their mistakes, and report levels of confidence in their choices that correlate with objective performance. These metacognitive assessments of decision quality are important for the guidance of behavior, particularly when external feedback is absent or sporadic. However, a computational framework that accounts for both confidence and error detection is lacking. In addition, accounts of dissociations between performance and metacognition have often relied on ad hoc assumptions, precluding a unified account of intact and impaired self-evaluation. Here we present a general Bayesian framework in which self-evaluation is cast as a "second-order" inference on a coupled but distinct decision system, computationally equivalent to inferring the performance of another actor. Second-order computation may ensue whenever there is a separation between internal states supporting decisions and confidence estimates over space and/or time. We contrast second-order computation against simpler first-order models in which the same internal state supports both decisions and confidence estimates. Through simulations we show that second-order computation provides a unified account of different types of self-evaluation often considered in separate literatures, such as confidence and error detection, and generates novel predictions about the contribution of one's own actions to metacognitive judgments. In addition, the model provides insight into why subjects' metacognition may sometimes be better or worse than task performance. We suggest that second-order computation may underpin self-evaluative judgments across a range of domains. (PsycINFO Database Record

The impact of evidence reliability on sensitivity and bias in decision confidence

Human observers effortlessly and accurately judge their probability of being correct in their decisions, suggesting that metacognitive evaluation is an integral part of decision making. It remains a challenge for most models of confidence, however, to explain how metacognitive judgments are formed and which internal signals influence them. While the decision-making literature has suggested that confidence is based on privileged access to the evidence that gives rise to the decision itself, other lines of research on confidence have commonly taken the view of a multicue model of confidence. The present study aims at manipulating one such cue: the perceived reliability of evidence supporting an initial decision. Participants made a categorical judgment of the average color of an array of eight colored shapes, for which we critically manipulated both the distance of the mean color from the category boundary (evidence strength) and the variability of colors across the eight shapes (evidence reliability). Our results indicate that evidence reliability has a stronger impact on confidence than evidence strength. Specifically, we found that evidence reliability affects metacognitive readout, the mapping from subjectively experienced certainty to expressed confidence, allowing participants to adequately adjust their confidence ratings to match changes in objective task performance across conditions.

People constantly face various types of decisions, which are commonly accompanied by an inherent feeling of (in)correctness: Just as realizing the tennis ball we played will most likely hit the net, we can feel more or less confident regarding our recent car purchase. People’s confidence judgments have been found to be surprisingly accurate. However, little is known about the underlying mechanisms that give rise to them. In this study, we suggest that variability in the information we receive from the outside world is of particular importance for how confident we feel in our decisions—more so than the extent to which evidence favors one over another choice option. Specifically, we find that this variability affects how people translate their internal feelings of certainty into the confidence judgments they express.

The influence of evidence volatility on choice, reaction time and confidence in a perceptual decision

Many decisions are thought to arise via the accumulation of noisy evidence to a threshold or bound. In perception, the mechanism explains the effect of stimulus strength, characterized by signal-to-noise ratio, on decision speed, accuracy and confidence. It also makes intriguing predictions about the noise itself. An increase in noise should lead to faster decisions, reduced accuracy and, paradoxically, higher confidence. To test these predictions, we introduce a novel sensory manipulation that mimics the addition of unbiased noise to motion-selective regions of visual cortex, which we verified with neuronal recordings from macaque areas MT/MST. For both humans and monkeys, increasing the noise induced faster decisions and greater confidence over a range of stimuli for which accuracy was minimally impaired. The magnitude of the effects was in agreement with predictions of a bounded evidence accumulation model.

DOI:http://dx.doi.org/10.7554/eLife.17688.001

Many of our decisions are made on the basis of imperfect or ‘noisy’ information. A longstanding goal in neuroscience is to work out how such noise affects three aspects of decision-making: the accuracy (or appropriateness) of a choice, the speed at which the choice is made, and the decision-maker’s confidence that they have chosen correctly.

One theory of decision-making is that the brain simultaneously accumulates evidence for each of the options it is considering, until one option exceeds a threshold and is declared the ‘winner’. This theory is known as bounded evidence accumulation. It predicts that increasing the noisiness of the available information decreases the accuracy of decisions made in response. Counterintuitively, it also predicts that such an increase in noise speeds up decision-making and increases confidence levels.

Zylberberg et al. have now tested these predictions experimentally by getting human volunteers and monkeys to perform a series of trials where they had to decide whether a set of randomly moving dots moved to the left or to the right overall. Using a newly developed method, the noisiness of the dot motion could be changed between trials. The effectiveness of this technique was confirmed by recording the activity of neurons in the region of the monkey brain that processes visual motion information.

After each trial, the humans rated their confidence in their decision. By comparison, the monkeys could indicate that they were not confident in a decision by opting for a guaranteed small reward on certain trials (instead of the larger reward they received when they correctly indicated the direction of motion of the dots).

In both humans and monkeys, increasing the noisiness associated with the movement of the dots led to faster and more confident decision-making, just as the bounded evidence accumulation framework predicts. Furthermore, the results presented by Zylberberg et al. suggest that the brain does not always gauge how reliable evidence is in order to fine-tune decisions.

Now that the role of noise in decision-making is better understood, future experiments could attempt to reveal how artificial manipulations of the brain contribute both information and noise to a decision. Other experiments might ascertain when the brain can learn that noisy information should invite slower, more cautious decisions.

DOI:http://dx.doi.org/10.7554/eLife.17688.002

Absolutely relative or relatively absolute: violations of value invariance in human decision making

Making decisions based on relative rather than absolute information processing is tied to choice optimality via the accumulation of evidence differences and to canonical neural processing via accumulation of evidence ratios. These theoretical frameworks predict invariance of decision latencies to absolute intensities that maintain differences and ratios, respectively. While information about the absolute values of the choice alternatives is not necessary for choosing the best alternative, it may nevertheless hold valuable information about the context of the decision. To test the sensitivity of human decision making to absolute values, we manipulated the intensities of brightness stimuli pairs while preserving either their differences or their ratios. Although asked to choose the brighter alternative relative to the other, participants responded faster to higher absolute values. Thus, our results provide empirical evidence for human sensitivity to task irrelevant absolute values indicating a hard-wired mechanism that precedes executive control. Computational investigations of several modelling architectures reveal two alternative accounts for this phenomenon, which combine absolute and relative processing. One account involves accumulation of differences with activation dependent processing noise and the other emerges from accumulation of absolute values subject to the temporal dynamics of lateral inhibition. The potential adaptive role of such choice mechanisms is discussed.

Visual Confidence

Visual confidence refers to an observer's ability to judge the accuracy of her perceptual decisions. Even though confidence judgments have been recorded since the early days of psychophysics, only recently have they been recognized as essential for a deeper understanding of visual perception. The reluctance to study visual confidence may have come in part from obtaining convincing experimental evidence in favor of metacognitive abilities rather than just perceptual sensitivity. Some effort has thus been dedicated to offer different experimental paradigms to study visual confidence in humans and nonhuman animals. To understand the origins of confidence judgments, investigators have developed two competing frameworks. The approach based on signal decision theory is popular but fails to account for response times. In contrast, the approach based on accumulation of evidence models naturally includes the dynamics of perceptual decisions. These models can explain a range of results, including the apparently paradoxical dissociation between performance and confidence that is sometimes observed.

A Mathematical Framework for Statistical Decision Confidence

Decision confidence is a forecast about the probability that a decision will be correct. From a statistical perspective, decision confidence can be defined as the Bayesian posterior probability that the chosen option is correct based on the evidence contributing to it. Here, we used this formal definition as a starting point to develop a normative statistical framework for decision confidence. Our goal was to make general predictions that do not depend on the structure of the noise or a specific algorithm for estimating confidence. We analytically proved several interrelations between statistical decision confidence and observable decision measures, such as evidence discriminability, choice, and accuracy. These interrelationships specify necessary signatures of decision confidence in terms of externally quantifiable variables that can be empirically tested. Our results lay the foundations for a mathematically rigorous treatment of decision confidence that can lead to a common framework for understanding confidence across different research domains, from human and animal behavior to neural representations.

Confidence through consensus: a neural mechanism for uncertainty monitoring

Models that integrate sensory evidence to a threshold can explain task accuracy, response times and confidence, yet it is still unclear how confidence is encoded in the brain. Classic models assume that confidence is encoded in some form of balance between the evidence integrated in favor and against the selected option. However, recent experiments that measure the sensory evidence’s influence on choice and confidence contradict these classic models. We propose that the decision is taken by many loosely coupled modules each of which represent a stochastic sample of the sensory evidence integral. Confidence is then encoded in the dispersion between modules. We show that our proposal can account for the well established relations between confidence, and stimuli discriminability and reaction times, as well as the fluctuations influence on choice and confidence.

A common mechanism underlies changes of mind about decisions and confidence

Decisions are accompanied by a degree of confidence that a selected option is correct. A sequential sampling framework explains the speed and accuracy of decisions and extends naturally to the confidence that the decision rendered is likely to be correct. However, discrepancies between confidence and accuracy suggest that confidence might be supported by mechanisms dissociated from the decision process. Here we show that this discrepancy can arise naturally because of simple processing delays. When participants were asked to report choice and confidence simultaneously, their confidence, reaction time and a perceptual decision about motion were explained by bounded evidence accumulation. However, we also observed revisions of the initial choice and/or confidence. These changes of mind were explained by a continuation of the mechanism that led to the initial choice. Our findings extend the sequential sampling framework to vacillation about confidence and invites caution in interpreting dissociations between confidence and accuracy.

DOI:http://dx.doi.org/10.7554/eLife.12192.001

To understand how the brain makes decisions is to understand how we think – how we deal with information, interpret it and agree with a particular interpretation of the information. Neuroscience has begun to uncover the mechanisms that underlie these processes by linking the activity of nerve cells in the brain to different aspects of making decisions. These include how long it takes to reach a decision, why we make errors and how confident we feel about a decision.

Sometimes when we make a decision and have committed to an answer, we then change our minds. Now, van den Berg et al. have asked whether the brain mechanisms that support a change of mind also support a change in confidence. To investigate this problem, human volunteers were asked to perform a difficult task where they had to decide whether a field of randomly moving dots had a tendency to drift to the left or to the right.

During the experiment, van den Berg et al. recorded how long the volunteers took to make their decision, how confident the volunteers felt about their choice, and whether they were correct. Analyzing this data revealed that all of these measures could be explained by a mechanism where the brain accumulates evidence only until there appears to be enough evidence to favor one choice over the other. This process specifies how confident an individual should be based on the quality of the sensory evidence and how long it takes to make a decision.

In addition, van den Berg et al. found that occasionally a volunteer changed their mind about how confident they were about a decision after they’d made it, as if they had continued to think about it. This was despite the volunteers receiving no more information about the task or how well they had done once they had made their decision. Therefore, it appears that the brain processed additional information that had already been detected but did not have time to affect the initial choice.

The activity of the nerve cells in the brain was not recorded as the volunteers made their decisions. Future experiments that incorporate these measurements could help reveal how the brain performs the necessary computations and account for the time delay seen in processing some of the data. Where is this delayed information processed in the brain, and how does it lead to a change of mind?

DOI:http://dx.doi.org/10.7554/eLife.12192.002

The Encoding of Decision Difficulty and Movement Time in the Primate Premotor Cortex

Estimating the difficulty of a decision is a fundamental process to elaborate complex and adaptive behaviour. In this paper, we show that the movement time of behaving monkeys performing a decision-making task is correlated with decision difficulty and that the activity of a population of neurons in ventral Premotor cortex correlates with the movement time. Moreover, we found another population of neurons that encodes the discriminability of the stimulus, thereby supplying another source of information about the difficulty of the decision. The activity of neurons encoding the difficulty can be produced by very different computations. Therefore, we show that decision difficulty can be encoded through three different mechanisms: 1. Switch time coding, 2. rate coding and 3. binary coding. This rich representation reflects the basis of different functional aspects of difficulty in the making of a decision and the possible role of difficulty estimation in complex decision scenarios.

Understanding how the brain produces complex cognitive functions has been a crucial question since ancient philosophical inquiries. The encoding of decision difficulty in the brain is fundamental for complex and adaptive behaviour, and can provide valuable information in uncertain environments where the future outcome of a choice must be evaluated beforehand. Here we show that neurons in premotor cortex represent the difficulty of a decision using at least three different variables: 1) the time of the neuronal response, 2) the intensity of the neuronal response, 3) the probability of switching from a low activity to a high activity profile. Moreover, we show that, by encoding the time elapsed from the end of the stimulus and commitment to a choice, another set of premotor neurons is able to provide information about the difficulty of the decision. These results show that the brain is implementing heterogeneous neural mechanisms to fulfill a complex cognitive function.

Confidence estimation as a stochastic process in a neurodynamical system of decision making

Evaluation of confidence about one's knowledge is key to the brain's ability to monitor cognition. To investigate the neural mechanism of confidence assessment, we examined a biologically realistic spiking network model and found that it reproduced salient behavioral observations and single-neuron activity data from a monkey experiment designed to study confidence about a decision under uncertainty. Interestingly, the model predicts that changes of mind can occur in a mnemonic delay when confidence is low; the probability of changes of mind increases (decreases) with task difficulty in correct (error) trials. Furthermore, a so-called "hard-easy effect" observed in humans naturally emerges, i.e., behavior shows underconfidence (underestimation of correct rate) for easy or moderately difficult tasks and overconfidence (overestimation of correct rate) for very difficult tasks. Importantly, in the model, confidence is computed using a simple neural signal in individual trials, without explicit representation of probability functions. Therefore, even a concept of metacognition can be explained by sampling a stochastic neural activity pattern.

Orbitofrontal cortex is required for optimal waiting based on decision confidence

Confidence judgments are a central example of metacognition-knowledge about one's own cognitive processes. According to this metacognitive view, confidence reports are generated by a second-order monitoring process based on the quality of internal representations about beliefs. Although neural correlates of decision confidence have been recently identified in humans and other animals, it is not well understood whether there are brain areas specifically important for confidence monitoring. To address this issue, we designed a postdecision temporal wagering task in which rats expressed choice confidence by the amount of time they were willing to wait for reward. We found that orbitofrontal cortex inactivation disrupts waiting-based confidence reports without affecting decision accuracy. Furthermore, we show that a normative model can quantitatively account for waiting times based on the computation of decision confidence. These results establish an anatomical locus for a metacognitive report, confidence judgment, distinct from the processes required for perceptual decisions.

Relation between belief and performance in perceptual decision making

In an uncertain and ambiguous world, effective decision making requires that subjects form and maintain a belief about the correctness of their choices, a process called meta-cognition. Prediction of future outcomes and self-monitoring are only effective if belief closely matches behavioral performance. Equality between belief and performance is also critical for experimentalists to gain insight into the subjects' belief by simply measuring their performance. Assuming that the decision maker holds the correct model of the world, one might indeed expect that belief and performance should go hand in hand. Unfortunately, we show here that this is rarely the case when performance is defined as the percentage of correct responses for a fixed stimulus, a standard definition in psychophysics. In this case, belief equals performance only for a very narrow family of tasks, whereas in others they will only be very weakly correlated. As we will see it is possible to restore this equality in specific circumstances but this remedy is only effective for a decision-maker, not for an experimenter. We furthermore show that belief and performance do not match when conditioned on task difficulty--as is common practice when plotting the psychometric curve--highlighting common pitfalls in previous neuroscience work. Finally, we demonstrate that miscalibration and the hard-easy effect observed in humans' and other animals' certainty judgments could be explained by a mismatch between the experimenter's and decision maker's expected distribution of task difficulties. These results have important implications for experimental design and are of relevance for theories that aim to unravel the nature of meta-cognition.

Supra-personal cognitive control and metacognition

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We propose a ‘dual systems’ framework for thinking about metacognition.

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System 1 metacognition is for ‘intra-personal’ cognitive control.

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System 2 metacognition is for ‘supra-personal’ cognitive control.

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The latter allows agents to share metacognitive representations.

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This sharing creates benefits for the group and facilitates cumulative culture.

The human mind is extraordinary in its ability not merely to respond to events as they unfold but also to adapt its own operation in pursuit of its agenda. This ‘cognitive control’ can be achieved through simple interactions among sensorimotor processes, and through interactions in which one sensorimotor process represents a property of another in an implicit, unconscious way. So why does the human mind also represent properties of cognitive processes in an explicit way, enabling us to think and say ‘I’m sure’ or ‘I’m doubtful’? We suggest that ‘system 2 metacognition’ is for supra-personal cognitive control. It allows metacognitive information to be broadcast, and thereby to coordinate the sensorimotor systems of two or more agents involved in a shared task.

The construction of confidence in a perceptual decision

Decision-making involves the selection of one out of many possible courses of action. A decision may bear on other decisions, as when humans seek a second medical opinion before undergoing a risky surgical intervention. These “meta-decisions” are mediated by confidence judgments—the degree to which decision-makers consider that a choice is likely to be correct. We studied how subjective confidence is constructed from noisy sensory evidence. The psychophysical kernels used to convert sensory information into choice and confidence decisions were precisely reconstructed measuring the impact of small fluctuations in sensory input. This is shown in two independent experiments in which human participants made a decision about the direction of motion of a set of randomly moving dots, or compared the brightness of a group of fluctuating bars, followed by a confidence report. The results of both experiments converged to show that: (1) confidence was influenced by evidence during a short window of time at the initial moments of the decision, and (2) confidence was influenced by evidence for the selected choice but was virtually blind to evidence for the non-selected choice. Our findings challenge classical models of subjective confidence—which posit that the difference of evidence in favor of each choice is the seed of the confidence signal.

A computational framework for the study of confidence in humans and animals

Confidence judgements, self-assessments about the quality of a subject's knowledge, are considered a central example of metacognition. Prima facie, introspection and self-report appear the only way to access the subjective sense of confidence or uncertainty. Contrary to this notion, overt behavioural measures can be used to study confidence judgements by animals trained in decision-making tasks with perceptual or mnemonic uncertainty. Here, we suggest that a computational approach can clarify the issues involved in interpreting these tasks and provide a much needed springboard for advancing the scientific understanding of confidence. We first review relevant theories of probabilistic inference and decision-making. We then critically discuss behavioural tasks employed to measure confidence in animals and show how quantitative models can help to constrain the computational strategies underlying confidence-reporting behaviours. In our view, post-decision wagering tasks with continuous measures of confidence appear to offer the best available metrics of confidence. Since behavioural reports alone provide a limited window into mechanism, we argue that progress calls for measuring the neural representations and identifying the computations underlying confidence reports. We present a case study using such a computational approach to study the neural correlates of decision confidence in rats. This work shows that confidence assessments may be considered higher order, but can be generated using elementary neural computations that are available to a wide range of species. Finally, we discuss the relationship of confidence judgements to the wider behavioural uses of confidence and uncertainty.

Computational models of decision making: integration, stability, and noise

Decision making demands the accumulation of sensory evidence over time. Questions remain about how this occurs, but recent years have seen progress on several fronts. The first concerns when optimal accumulation of evidence coincides with the simplest method of accumulating neural activity: summation over time. The second involves what computations the brain might perform when summation is difficult due to imprecision in neural circuits or is suboptimal due to uncertainty or variability in how evidence arrives. Finally, the third concerns sources of noise in decision circuits. Empirical studies have better constrained the extent of this noise, and modeling work is helping to clarify its possible origins.

The cost of accumulating evidence in perceptual decision making

Decision making often involves the accumulation of information over time, but acquiring information typically comes at a cost. Little is known about the cost incurred by animals and humans for acquiring additional information from sensory variables due, for instance, to attentional efforts. Through a novel integration of diffusion models and dynamic programming, we were able to estimate the cost of making additional observations per unit of time from two monkeys and six humans in a reaction time (RT) random-dot motion discrimination task. Surprisingly, we find that the cost is neither zero nor constant over time, but for the animals and humans features a brief period in which it is constant but increases thereafter. In addition, we show that our theory accurately matches the observed reaction time distributions for each stimulus condition, the time-dependent choice accuracy both conditional on stimulus strength and independent of it, and choice accuracy and mean reaction times as a function of stimulus strength. The theory also correctly predicts that urgency signals in the brain should be independent of the difficulty, or stimulus strength, at each trial.

Cortical attractor network dynamics with diluted connectivity

The connectivity of the cerebral cortex is diluted, with the probability of excitatory connections between even nearby pyramidal cells rarely more than 0.1, and in the hippocampus 0.04. To investigate the extent to which this diluted connectivity affects the dynamics of attractor networks in the cerebral cortex, we simulated an integrate-and-fire attractor network taking decisions between competing inputs with diluted connectivity of 0.25 or 0.1, and with the same number of synaptic connections per neuron for the recurrent collateral synapses within an attractor population as for full connectivity. The results indicated that there was less spiking-related noise with the diluted connectivity in that the stability of the network when in the spontaneous state of firing increased, and the accuracy of the correct decisions increased. The decision times were a little slower with diluted than with complete connectivity. Given that the capacity of the network is set by the number of recurrent collateral synaptic connections per neuron, on which there is a biological limit, the findings indicate that the stability of cortical networks, and the accuracy of their correct decisions or memory recall operations, can be increased by utilizing diluted connectivity and correspondingly increasing the number of neurons in the network, with little impact on the speed of processing of the cortex. Thus diluted connectivity can decrease cortical spiking-related noise. In addition, we show that the Fano factor for the trial-to-trial variability of the neuronal firing decreases from the spontaneous firing state value when the attractor network makes a decision. This article is part of a Special Issue entitled "Neural Coding".

Decision-making, errors, and confidence in the brain

To provide a fundamental basis for understanding decision-making and decision confidence, we analyze a neuronal spiking attractor-based model of decision-making. The model predicts probabilistic decision-making with larger neuronal responses and larger functional magnetic resonance imaging (fMRI) blood-oxygen-level-dependent (BOLD) responses on correct than on error trials because the spiking noise-influenced decision attractor state of the network is consistent with the external evidence. Moreover, the model predicts that the neuronal activity and the BOLD response will become larger on correct trials as the discriminability ΔI increases and confidence increases and will become smaller as confidence decreases on error trials as ΔI increases. Confidence is thus an emergent property of the model. In an fMRI study of an olfactory decision-making task, we confirm these predictions for cortical areas including medial prefrontal cortex and the cingulate cortex implicated in choice decision-making, showing a linear increase in the BOLD signal with ΔI on correct trials, and a linear decrease on error trials. These effects were not found in a control area, the orbitofrontal cortex, where reward value useful for the choice is represented on a continuous scale but that is not implicated in the choice itself. This provides a unifying approach to decision-making and decision confidence and to how spiking-related noise affects choice, confidence, synaptic and neuronal activity, and fMRI signals.