BCI Toolbox: An open-source python package for the Bayesian causal inference model.

Psychological and neuroscientific research over the past two decades has shown that the Bayesian causal inference (BCI) is a potential unifying theory that can account for a wide range of perceptual and sensorimotor processes in humans. Therefore, we introduce the BCI Toolbox, a statistical and analytical tool in Python, enabling researchers to conveniently perform quantitative modeling and analysis of behavioral data. Additionally, we describe the algorithm of the BCI model and test its stability and reliability via parameter recovery. The present BCI toolbox offers a robust platform for BCI model implementation as well as a hands-on tool for learning and understanding the model, facilitating its widespread use and enabling researchers to delve into the data to uncover underlying cognitive mechanisms.

Developmental changes in colour constancy in a naturalistic object selection task.

When the illumination falling on a surface change, so does the reflected light. Despite this, adult observers are good at perceiving surfaces as relatively unchanging-an ability termed colour constancy. Very few studies have investigated colour constancy in infants, and even fewer in children. Here we asked whether there is a difference in colour constancy between children and adults; what the developmental trajectory is between six and 11 years; and whether the pattern of constancy across illuminations and reflectances differs between adults and children. To this end, we developed a novel, child-friendly computer-based object selection task. In this, observers saw a dragon's favourite sweet under a neutral illumination and picked the matching sweet from an array of eight seen under a different illumination (blue, yellow, red, or green). This set contained a reflectance match (colour constant; perfect performance) and a tristimulus match (colour inconstant). We ran two experiments, with two-dimensional scenes in one and three-dimensional renderings in the other. Twenty-six adults and 33 children took part in the first experiment; 26 adults and 40 children took part in the second. Children performed better than adults on this task, and their performance decreased with age in both experiments. We found differences across illuminations and sweets, but a similar pattern across both age groups. This unexpected finding might reflect a real decrease in colour constancy from childhood to adulthood, explained by developmental changes in the perceptual and cognitive mechanisms underpinning colour constancy, or differences in task strategies between children and adults. HIGHLIGHTS: Six- to 11-year-old children demonstrated better performance than adults on a colour constancy object selection task. Performance decreased with age over childhood. These findings may indicate development of cognitive strategies used to overcome automatic colour constancy mechanisms.

Newly learned shape-color associations show signatures of reliability-weighted averaging without forced fusion or a memory color effect.

Reliability-weighted averaging of multiple perceptual estimates (or cues) can improve precision. Research suggests that newly learned statistical associations can be rapidly integrated in this way for efficient decision-making. Yet, it remains unclear if the integration of newly learned statistics into decision-making can directly influence perception, rather than taking place only at the decision stage. In two experiments, we implicitly taught observers novel associations between shape and color. Observers made color matches by adjusting the color of an oval to match a simultaneously presented reference. As the color of the oval changed across trials, so did its shape according to a novel mapping of axis ratio to color. Observers showed signatures of reliability-weighted averaging-a precision improvement in both experiments and reweighting of the newly learned shape cue with changes in uncertainty in Experiment 2. To ask whether this was accompanied by perceptual effects, Experiment 1 tested for forced fusion by measuring color discrimination thresholds with and without incongruent novel cues. Experiment 2 tested for a memory color effect, observers adjusting the color of ovals with different axis ratios until they appeared gray. There was no evidence for forced fusion and the opposite of a memory color effect. Overall, our results suggest that the ability to quickly learn novel cues and integrate them with familiar cues is not immediately (within the short duration of our experiments and in the domain of color and shape) accompanied by common perceptual effects.

Central tendency biases must be accounted for to consistently capture Bayesian cue combination in continuous response data.

Observers in perceptual tasks are often reported to combine multiple sensory cues in a weighted average that improves precision-in some studies, approaching statistically optimal (Bayesian) weighting, but in others departing from optimality, or not benefitting from combined cues at all. To correctly conclude which combination rules observers use, it is crucial to have accurate measures of their sensory precision and cue weighting. Here, we present a new approach for accurately recovering these parameters in perceptual tasks with continuous responses. Continuous responses have many advantages, but are susceptible to a central tendency bias, where responses are biased towards the central stimulus value. We show that such biases lead to inaccuracies in estimating both precision gains and cue weightings, two key measures used to assess sensory cue combination. We introduce a method that estimates sensory precision by regressing continuous responses on targets and dividing the variance of the residuals by the squared slope of the regression line, "correcting-out" the error introduced by the central bias and increasing statistical power. We also suggest a complementary analysis that recovers the sensory cue weights. Using both simulations and empirical data, we show that the proposed methods can accurately estimate sensory precision and cue weightings in the presence of central tendency biases. We conclude that central tendency biases should be (and can easily be) accounted for to consistently capture Bayesian cue combination in continuous response data.

Using Occam's razor and Bayesian modelling to compare discrete and continuous representations in numerosity judgements.

Previous research has established that numeric estimates are based not just on perceptual data but also past experience, and so may be influenced by the form of this stored information. It remains unclear, however, how such experience is represented: numerical data can be processed by either a continuous analogue number system or a discrete symbolic number system, with each predicting different generalisation effects. The present paper therefore contrasts discrete and continuous prior formats within the domain of numerical estimation using both direct comparisons of computational models of this process using these representations, as well as empirical contrasts exploiting different predicted reactions of these formats to uncertainty via Occam's razor. Both computational and empirical results indicate that numeric estimates commonly rely on a continuous prior format, mirroring the analogue approximate number system, or 'number sense'. This implies a general preference for the use of continuous numerical representations even where both stimuli and responses are discrete, with learners seemingly relying on innate number systems rather than the symbolic forms acquired in later life. There is however remaining uncertainty in these results regarding individual differences in the use of these systems, which we address in recommendations for future work.

Bayesian transfer in a complex spatial localization task.

Prior knowledge can help observers in various situations. Adults can simultaneously learn two location priors and integrate these with sensory information to locate hidden objects. Importantly, observers weight prior and sensory (likelihood) information differently depending on their respective reliabilities, in line with principles of Bayesian inference. Yet, there is limited evidence that observers actually perform Bayesian inference, rather than a heuristic, such as forming a look-up table. To distinguish these possibilities, we ask whether previously learned priors will be immediately integrated with a new, untrained likelihood. If observers use Bayesian principles, they should immediately put less weight on the new, less reliable, likelihood ("Bayesian transfer"). In an initial experiment, observers estimated the position of a hidden target, drawn from one of two distinct distributions, using sensory and prior information. The sensory cue consisted of dots drawn from a Gaussian distribution centered on the true location with either low, medium, or high variance; the latter introduced after block three of five to test for evidence of Bayesian transfer. Observers did not weight the cue (relative to the prior) significantly less in the high compared to medium variance condition, counter to Bayesian predictions. However, when explicitly informed of the different prior variabilities, observers placed less weight on the new high variance likelihood ("Bayesian transfer"), yet, substantially diverged from ideal. Much of this divergence can be captured by a model that weights sensory information, according only to internal noise in using the cue. These results emphasize the limits of Bayesian models in complex tasks.

Specular highlights improve color constancy when other cues are weakened.

Previous studies suggest that to achieve color constancy, the human visual system makes use of multiple cues, including a priori assumptions about the illumination ("daylight priors"). Specular highlights have been proposed to aid constancy, but the evidence for their usefulness is mixed. Here, we used a novel cue-combination approach to test whether the presence of specular highlights or the validity of a daylight prior improves illumination chromaticity estimates, inferred from achromatic settings, to determine whether and under which conditions either cue contributes to color constancy. Observers made achromatic settings within three-dimensional rendered scenes containing matte or glossy shapes, illuminated by either daylight or nondaylight illuminations. We assessed both the variability of these settings and their accuracy, in terms of the standard color constancy index (CCI). When a spectrally uniform background was present, neither CCIs nor variability improved with specular highlights or daylight illuminants (Experiment 1). When a Mondrian background was introduced, CCIs decreased overall but were higher for scenes containing glossy, as opposed to matte, shapes (Experiments 2 and 3). There was no overall reduction in variability of settings and no benefit for scenes illuminated by daylights. Taken together, these results suggest that the human visual system indeed uses specular highlights to improve color constancy but only when other cues, such as from the local surround, are weakened.

Fast and Accurate Learning When Making Discrete Numerical Estimates.

Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates.

The overlooked role of unisensory precision in multisensory research.

Zhu et al. present an alternative explanation for the weaker multisensory illusions in football goalkeepers compared with outfielders and non-athletes, showing that better unisensory precision in goalkeepers can also account for this effect.

Proximity to rewards modulates parameters of effortful control exertion.

The now-classic goal-gradient hypothesis posits that organisms increase effort expenditure as a function of their proximity to a goal. Despite nearly a century having passed since its original formulation, goal-gradient-like behavior in human cognitive performance remains poorly understood: Are we more willing to engage in costly cognitive processing when we are near, versus far, from a goal state? Moreover, the computational mechanisms underpinning these potential goal-gradient effects-for example, whether goal proximity affects fidelity of stimulus encoding, response caution, or other identifiable mechanisms governing speed and accuracy-are unclear. Here, in two experiments, we examine the effect of goal proximity, operationalized as progress toward the completion of a rewarded task block, upon task performance in an attentionally demanding oddball task. Supporting the goal-gradient hypothesis, we found that participants responded more quickly, but not less accurately, when rewards were proximal than when they were distal. Critically, this effect was only observed when participants were given information about goal proximity. Using hierarchical drift diffusion modeling, we found that these apparent goal-gradient performance effects were best explained by a collapsing bound model, in which proximity to a goal reduced response caution and increased information processing. Taken together, these results suggest that goal gradients could help explain the oft-observed fluctuations in engagement of cognitively effortful processing, extending the scope of the goal-gradient hypothesis to the domain of cognitive tasks. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Different types of uncertainty in multisensory perceptual decision making.

Efficient decision-making requires accounting for sources of uncertainty (noise, or variability). Many studies have shown how the nervous system is able to account for perceptual uncertainty (noise, variability) that arises from limitations in its own abilities to encode perceptual stimuli. However, many other sources of uncertainty exist, reflecting for example variability in the behaviour of other agents or physical processes. Here we review previous studies on decision making under uncertainty as a function of the different types of uncertainty that the nervous system encounters, showing that noise that is intrinsic to the perceptual system can often be accounted for near-optimally (i.e. not statistically different from optimally), whereas accounting for other types of uncertainty can be much more challenging. As an example, we present a study in which participants made decisions about multisensory stimuli with both intrinsic (perceptual) and extrinsic (environmental) uncertainty and show that the nervous system accounts for these differently when making decisions: they account for internal uncertainty but under-account for external. Human perceptual systems may be well equipped to account for intrinsic (perceptual) uncertainty because, in principle, they have access to this. Accounting for external uncertainty is more challenging because this uncertainty must be learned. This article is part of the theme issue 'Decision and control processes in multisensory perception'.

A presaccadic perceptual impairment at the postsaccadic location of the blindspot.

Saccadic eye movements are preceded by profound changes in visual perception. These changes have been linked to the phenomenon of 'forward remapping', in which cells begin to respond to stimuli that appear in their post-saccadic receptive field before the eye has moved. Few studies have examined the perceptual consequences of remapping of areas of impaired sensory acuity, such as the blindspot. Understanding the perceptual consequences of remapping of scotomas may produce important insights into why some neurovisual deficits, such as hemianopia are so intractable for rehabilitation. The current study took advantage of a naturally occurring scotoma in healthy participants (the blindspot) to examine pre-saccadic perception at the upcoming location of the blindspot. Participants viewed stimuli monocularly and were required to make stimulus-driven vertical eye-movements. At a variable latency between the onset of saccade target (ST) and saccade execution a discrimination target (DT) was presented at one of 4 possible locations; within the blindspot, contralateral to the blindspot, in post-saccadic location of the blindspot and contralateral to the post-saccadic location of the blindspot. There was a significant perceptual impairment at the post-saccadic location of the blindspot relative to the contralateral post-saccadic location of the blindspot and the post-saccadic location of the blindspot in a no-saccade control condition. These data are consistent with the idea that the visual system includes a representation of the blindspot which is remapped prior to saccade onset.

Bayesian causal inference: A unifying neuroscience theory.

Understanding of the brain and the principles governing neural processing requires theories that are parsimonious, can account for a diverse set of phenomena, and can make testable predictions. Here, we review the theory of Bayesian causal inference, which has been tested, refined, and extended in a variety of tasks in humans and other primates by several research groups. Bayesian causal inference is normative and has explained human behavior in a vast number of tasks including unisensory and multisensory perceptual tasks, sensorimotor, and motor tasks, and has accounted for counter-intuitive findings. The theory has made novel predictions that have been tested and confirmed empirically, and recent studies have started to map its algorithms and neural implementation in the human brain. The parsimony, the diversity of the phenomena that the theory has explained, and its illuminating brain function at all three of Marr's levels of analysis make Bayesian causal inference a strong neuroscience theory. This also highlights the importance of collaborative and multi-disciplinary research for the development of new theories in neuroscience.

Newly learned novel cues to location are combined with familiar cues but not always with each other.

Mature perceptual systems can learn new arbitrary sensory signals (novel cues) to properties of the environment, but little is known about the extent to which novel cues are integrated into normal perception. In normal perception, multiple uncertain familiar cues are combined, often near-optimally (reliability-weighted averaging), to increase perceptual precision. We trained observers to use abstract novel cues to estimate horizontal locations of hidden objects on a monitor. In experiment 1, 4 groups of observers each learned to use a different novel cue. All groups benefited from a suboptimal but significant gain in precision using novel and familiar cues together after short-term training (3 ∼1.5 hr sessions), extending previous reports of novel-familiar cue combination. In experiment 2, we tested whether 2 novel cues may also be combined with each other. One pair of novel cues could be combined to improve precision but the other could not, at least not after 3 sessions of repeated training. Overall, our results provide extensive evidence that novel cues can be learned and combined with familiar cues to enhance perception, but mixed evidence for whether perceptual and decision-making systems can extend this ability to the combination of multiple novel cues with only short-term training. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Detecting a viewer's familiarity with a face: Evidence from event-related brain potentials and classifier analyses.

Human observers recognize the faces of people they know efficiently and without apparent effort. Consequently, recognizing a familiar face is often assumed to be an automatic process beyond voluntary control. However, there are circumstances in which a person might seek to hide their recognition of a particular face. The present study therefore used event-related potentials (ERPs) and a classifier based on logistic regression to determine if it is possible to detect whether a viewer is familiar with a particular face, regardless of whether the participant is willing to acknowledge it or not. In three experiments, participants were presented with highly variable "ambient" images of personally familiar and unfamiliar faces, while performing an incidental butterfly detection task (Experiment 1), an explicit familiarity judgment task (Experiment 2), and a concealed familiarity task in which they were asked to deny familiarity with one truly known facial identity while acknowledging familiarity with a second known identity (Experiment 3). In all three experiments, we observed substantially more negative ERP amplitudes at occipito-temporal electrodes for familiar relative to unfamiliar faces starting approximately 200 ms after stimulus onset. Both the earlier N250 familiarity effect, reflecting visual recognition of a known face, and the later sustained familiarity effect, reflecting the integration of visual with additional identity-specific information, were similar across experiments and thus independent of task demands. These results were further supported by the classifier analysis. We conclude that ERP correlates of familiar face recognition are largely independent of voluntary control and discuss potential applications in forensic settings.

Dopamine and reward-related vigor in younger and older adults.

Vigor reflects how motivated people are to respond to stimuli. We previously showed that, on average, humans are more vigorous when a higher rate of reward is available, and that this relationship is modulated by the dopamine precursor levodopa. Dopamine signaling and probabilistic reward learning deteriorate across the adult life span, and thus, the relationship between vigor and reward may also change in aging. We tested this assertion and assessed whether it correlates with D1 dopamine receptor availability, measured using Positron Emission Tomography. We registered response times of 30 older and 30 younger participants during an oddball discrimination task where rewards varied systematically between trials. The average reward rate had a similar impact on vigor in both age groups. There was a weak positive association between ventral striatal dopamine receptor availability and the effect of average reward rate on response time. Overall, the effect of reward on response vigor was similar in younger and older adults, and weakly correlated with dopamine D1 receptor availability.

Vigor in the face of fluctuating rates of reward: an experimental examination.

Two fundamental questions underlie the expression of behavior, namely what to do and how vigorously to do it. The former is the topic of an overwhelming wealth of theoretical and empirical work particularly in the fields of reinforcement learning and decision-making, with various forms of affective prediction error playing key roles. Although vigor concerns motivation, and so is the subject of many empirical studies in diverse fields, it has suffered a dearth of computational models. Recently, Niv et al. [Niv, Y., Daw, N. D., Joel, D., & Dayan, P. Tonic dopamine: Opportunity costs and the control of response vigor. Psychopharmacology (Berlin), 191, 507-520, 2007] suggested that vigor should be controlled by the opportunity cost of time, which is itself determined by the average rate of reward. This coupling of reward rate and vigor can be shown to be optimal under the theory of average return reinforcement learning for a particular class of tasks but may also be a more general, perhaps hard-wired, characteristic of the architecture of control. We, therefore, tested the hypothesis that healthy human participants would adjust their RTs on the basis of the average rate of reward. We measured RTs in an odd-ball discrimination task for rewards whose magnitudes varied slowly but systematically. Linear regression on the subjects' individual RTs using the time varying average rate of reward as the regressor of interest, and including nuisance regressors such as the immediate reward in a round and in the preceding round, showed that a significant fraction of the variance in subjects' RTs could indeed be explained by the rate of experienced reward. This validates one of the key proposals associated with the model, illuminating an apparently mandatory form of coupling that may involve tonic levels of dopamine.

Separate encoding of model-based and model-free valuations in the human brain.

Behavioral studies have long shown that humans solve problems in two ways, one intuitive and fast (System 1, model-free), and the other reflective and slow (System 2, model-based). The neurobiological basis of dual process problem solving remains unknown due to challenges of separating activation in concurrent systems. We present a novel neuroeconomic task that predicts distinct subjective valuation and updating signals corresponding to these two systems. We found two concurrent value signals in human prefrontal cortex: a System 1 model-free reinforcement signal and a System 2 model-based Bayesian signal. We also found a System 1 updating signal in striatal areas and a System 2 updating signal in lateral prefrontal cortex. Further, signals in prefrontal cortex preceded choices that are optimal according to either updating principle, while signals in anterior cingulate cortex and globus pallidus preceded deviations from optimal choice for reinforcement learning. These deviations tended to occur when uncertainty regarding optimal values was highest, suggesting that disagreement between dual systems is mediated by uncertainty rather than conflict, confirming recent theoretical proposals.

The human prefrontal cortex mediates integration of potential causes behind observed outcomes.

Prefrontal cortex has long been implicated in tasks involving higher order inference in which decisions must be rendered, not only about which stimulus is currently rewarded, but also which stimulus dimensions are currently relevant. However, the precise computational mechanisms used to solve such tasks have remained unclear. We scanned human participants with functional MRI, while they performed a hierarchical intradimensional/extradimensional shift task to investigate what strategy subjects use while solving higher order decision problems. By using a computational model-based analysis, we found behavioral and neural evidence that humans solve such problems not by occasionally shifting focus from one to the other dimension, but by considering multiple explanations simultaneously. Activity in human prefrontal cortex was better accounted for by a model that integrates over all available evidences than by a model in which attention is selectively gated. Importantly, our model provides an explanation for how the brain determines integration weights, according to which it could distribute its attention. Our results demonstrate that, at the point of choice, the human brain and the prefrontal cortex in particular are capable of a weighted integration of information across multiple evidences.

Pavlovian-instrumental interaction in 'observing behavior'.

Subjects typically choose to be presented with stimuli that predict the existence of future reinforcements. This so-called 'observing behavior' is evident in many species under various experimental conditions, including if the choice is expensive, or if there is nothing that subjects can do to improve their lot with the information gained. A recent study showed that the activities of putative midbrain dopamine neurons reflect this preference for observation in a way that appears to challenge the common prediction-error interpretation of these neurons. In this paper, we provide an alternative account according to which observing behavior arises from a small, possibly Pavlovian, bias associated with the operation of working memory.