Ubiquitous log odds: a common representation of probability and frequency distortion in perception, action, and cognition

Distinct basal ganglia contributions to learning from implicit and explicit value signals in perceptual decision-making

Metacognitive evaluations of confidence provide an estimate of decision accuracy that could guide learning in the absence of explicit feedback. We examine how humans might learn from this implicit feedback in direct comparison with that of explicit feedback, using simultaneous EEG-fMRI. Participants performed a motion direction discrimination task where stimulus difficulty was increased to maintain performance, with intermixed explicit- and no-feedback trials. We isolate single-trial estimates of post-decision confidence using EEG decoding, and find these neural signatures re-emerge at the time of feedback together with separable signatures of explicit feedback. We identified these signatures of implicit versus explicit feedback along a dorsal-ventral gradient in the striatum, a finding uniquely enabled by an EEG-fMRI fusion. These two signals appear to integrate into an aggregate representation in the external globus pallidus, which could broadcast updates to improve cortical decision processing via the thalamus and insular cortex, irrespective of the source of feedback.

Dissecting Bayes: Using influence measures to test normative use of probability density information derived from a sample

Bayesian decision theory (BDT) is frequently used to model normative performance in perceptual, motor, and cognitive decision tasks where the possible outcomes of actions are associated with rewards or penalties. The resulting normative models specify how decision makers should encode and combine information about uncertainty and value-step by step-in order to maximize their expected reward. When prior, likelihood, and posterior are probabilities, the Bayesian computation requires only simple arithmetic operations: addition, etc. We focus on visual cognitive tasks where Bayesian computations are carried out not on probabilities but on (1) probability density functions and (2) these probability density functions are derived from samples. We break the BDT model into a series of computations and test human ability to carry out each of these computations in isolation. We test three necessary properties of normative use of pdf information derived from a sample-accuracy, additivity and influence. Influence measures allow us to assess how much weight each point in the sample is assigned in making decisions and allow us to compare normative use (weighting) of samples to actual, point by point. We find that human decision makers violate accuracy and additivity systematically but that the cost of failure in accuracy or additivity would be minor in common decision tasks. However, a comparison of measured influence for each sample point with normative influence measures demonstrates that the individual's use of sample information is markedly different from the predictions of BDT. We will show that the normative BDT model takes into account the geometric symmetries of the pdf while the human decision maker does not. An alternative model basing decisions on a single extreme sample point provided a better account for participants' data than the normative BDT model.

A comparison of human and GPT-4 use of probabilistic phrases in a coordination game

English speakers use probabilistic phrases such as likely to communicate information about the probability or likelihood of events. Communication is successful to the extent that the listener grasps what the speaker means to convey and, if communication is successful, individuals can potentially coordinate their actions based on shared knowledge about uncertainty. We first assessed human ability to estimate the probability and the ambiguity (imprecision) of twenty-three probabilistic phrases in a coordination game in two different contexts, investment advice and medical advice. We then had GPT-4 (OpenAI), a Large Language Model, complete the same tasks as the human participants. We found that GPT-4's estimates of probability both in the Investment and Medical Contexts were as close or closer to that of the human participants as the human participants' estimates were to one another. However, further analyses of residuals disclosed small but significant differences between human and GPT-4 performance. Human probability estimates were compressed relative to those of GPT-4. Estimates of probability for both the human participants and GPT-4 were little affected by context. We propose that evaluation methods based on coordination games provide a systematic way to assess what GPT-4 and similar programs can and cannot do.

How do humans learn about the reliability of automation?

In a range of settings, human operators make decisions with the assistance of automation, the reliability of which can vary depending upon context. Currently, the processes by which humans track the level of reliability of automation are unclear. In the current study, we test cognitive models of learning that could potentially explain how humans track automation reliability. We fitted several alternative cognitive models to a series of participants' judgements of automation reliability observed in a maritime classification task in which participants were provided with automated advice. We examined three experiments including eight between-subjects conditions and 240 participants in total. Our results favoured a two-kernel delta-rule model of learning, which specifies that humans learn by prediction error, and respond according to a learning rate that is sensitive to environmental volatility. However, we found substantial heterogeneity in learning processes across participants. These outcomes speak to the learning processes underlying how humans estimate automation reliability and thus have implications for practice.

The parieto-occipital cortex is a candidate neural substrate for the human ability to approximate Bayesian inference

Adaptive decision-making often requires one to infer unobservable states based on incomplete information. Bayesian logic prescribes that individuals should do so by estimating the posterior probability by integrating the prior probability with new information, but the neural basis of this integration is incompletely understood. We record fMRI during a task in which participants infer the posterior probability of a hidden state while we independently modulate the prior probability and likelihood of evidence regarding the state; the task incentivizes participants to make accurate inferences and dissociates expected value from posterior probability. Here we show that activation in a region of left parieto-occipital cortex independently tracks the subjective posterior probability, combining its subcomponents of prior probability and evidence likelihood, and reflecting the individual participants' systematic deviations from objective probabilities. The parieto-occipital cortex is thus a candidate neural substrate for humans' ability to approximate Bayesian inference by integrating prior beliefs with new information.

A multi-stage anticipated surprise model with dynamic expectation for economic decision-making

There are many modeling works that aim to explain people's behaviors that violate classical economic theories. However, these models often do not take into full account the multi-stage nature of real-life problems and people's tendency in solving complicated problems sequentially. In this work, we propose a descriptive decision-making model for multi-stage problems with perceived post-decision information. In the model, decisions are chosen based on an entity which we call the 'anticipated surprise'. The reference point is determined by the expected value of the possible outcomes, which we assume to be dynamically changing during the mental simulation of a sequence of events. We illustrate how our formalism can help us understand prominent economic paradoxes and gambling behaviors that involve multi-stage or sequential planning. We also discuss how neuroscience findings, like prediction error signals and introspective neuronal replay, as well as psychological theories like affective forecasting, are related to the features in our model. This provides hints for future experiments to investigate the role of these entities in decision-making.

Are we really Bayesian? Probabilistic inference shows sub-optimal knowledge transfer

Numerous studies have found that the Bayesian framework, which formulates the optimal integration of the knowledge of the world (i.e. prior) and current sensory evidence (i.e. likelihood), captures human behaviours sufficiently well. However, there are debates regarding whether humans use precise but cognitively demanding Bayesian computations for behaviours. Across two studies, we trained participants to estimate hidden locations of a target drawn from priors with different levels of uncertainty. In each trial, scattered dots provided noisy likelihood information about the target location. Participants showed that they learned the priors and combined prior and likelihood information to infer target locations in a Bayes fashion. We then introduced a transfer condition presenting a trained prior and a likelihood that has never been put together during training. How well participants integrate this novel likelihood with their learned prior is an indicator of whether participants perform Bayesian computations. In one study, participants experienced the newly introduced likelihood, which was paired with a different prior, during training. Participants changed likelihood weighting following expected directions although the degrees of change were significantly lower than Bayes-optimal predictions. In another group, the novel likelihoods were never used during training. We found people integrated a new likelihood within (interpolation) better than the one outside (extrapolation) the range of their previous learning experience and they were quantitatively Bayes-suboptimal in both. We replicated the findings of both studies in a validation dataset. Our results showed that Bayesian behaviours may not always be achieved by a full Bayesian computation. Future studies can apply our approach to different tasks to enhance the understanding of decision-making mechanisms.

Perceptual anchoring effects: Evidence of response bias and a change in estimates sensitivity

INTRODUCTION

People's estimates of perceptual quantities are commonly biased by the contextual presence of other quantities (like numbers). In this study, we address assimilation anchoring effects (approximation of real quantities to contextual quantities) that occur for visually displayed proportions, defining a new methodological setting for the effect.

METHOD

Similar to classic approaches, we asked participants across several trials whether the display contained a feature in a proportion higher or lower than "a randomly selected value" (relative judgments), and then estimated the feature proportions (absolute judgments). Across all trials, we presented seven anchors ranging from .20 to .80, each with a visually displayed representation of the same seven proportions (49 judgments in total). This allowed for a psychophysical approach to individual estimates and signal detection indexes, providing new insights into how the anchoring effect is generated in this setting.

RESULTS

Our findings suggest that anchoring effects occur both as a bias (changes in response criteria) and as a change in the ability to discriminate stimuli (affecting sensitivity indexes). Moreover, anchors modulate the level of stimuli features for which estimates were more uncertain. Finally, our results indicate that anchor effects occur immediately in the first phase of the two-phase paradigm, leading to the availability of values for supporting absolute estimates.

CONCLUSION

By using a psychophysical approach to the anchoring effects, for the first time, we could clarify that this effect is the result of both bias and changes in the ability to discriminate quantity.

Pleiotropic contribution of rbfox1 to psychiatric and neurodevelopmental phenotypes in a zebrafish model

RBFOX1 is a highly pleiotropic gene that contributes to several psychiatric and neurodevelopmental disorders. Both rare and common variants in RBFOX1 have been associated with several psychiatric conditions, but the mechanisms underlying the pleiotropic effects of RBFOX1 are not yet understood. Here we found that, in zebrafish, rbfox1 is expressed in spinal cord, mid- and hindbrain during developmental stages. In adults, expression is restricted to specific areas of the brain, including telencephalic and diencephalic regions with an important role in receiving and processing sensory information and in directing behaviour. To investigate the effect of rbfox1 deficiency on behaviour, we used rbfox1sa15940, a rbfox1 loss-of-function line. We found that rbfox1sa15940 mutants present hyperactivity, thigmotaxis, decreased freezing behaviour and altered social behaviour. We repeated these behavioural tests in a second rbfox1 loss-of-function line with a different genetic background, rbfox1del19, and found that rbfox1 deficiency affects behaviour similarly in this line, although there were some differences. rbfox1del19 mutants present similar thigmotaxis, but stronger alterations in social behaviour and lower levels of hyperactivity than rbfox1sa15940 fish. Taken together, these results suggest that rbfox1 deficiency leads to multiple behavioural changes in zebrafish that might be modulated by environmental, epigenetic and genetic background effects, and that resemble phenotypic alterations present in Rbfox1-deficient mice and in patients with different psychiatric conditions. Our study thus highlights the evolutionary conservation of rbfox1 function in behaviour and paves the way to further investigate the mechanisms underlying rbfox1 pleiotropy on the onset of neurodevelopmental and psychiatric disorders.

A standardised set of images for judgements of proportion

In the present work, we present normative data for a set of 39 original clipart-style images that can be used as material in studies involving judgements of proportion. The original images are drawings that depict different day-to-day scenarios (e.g., lighted windows in a building; books on a shelf) and each has seven variants of different proportions (from 20% to 80%) belonging to different categories (discrete vs continuous; social vs non-social; natural vs artificial; stimuli physical dimensions; number of referents). Normative data for these images are presented in an interactive database (available at https://judgment-images-and-norms.shinyapps.io/estimates_interactive/ ), corresponding to the means of proportion estimates (in percentage form), the perceived ease of making such estimates, the perceived level of familiarity and liking for each image, and the relationships between these variables. In the paper, we analyse the data at an individual level, addressing how the latter judgements are related to the proportion estimates, how those estimates are related to objective proportions, and how these relationships are moderated by image category. The analyses presented in this paper aim to aid readers in selecting images that enable them to better address specific influences on proportional estimates or to control for those influences in their studies.

Effects of the COVID-19 Pandemic on Neural Responses to Reward: A Quasi-experiment

BACKGROUND

The COVID-19 pandemic has been a prolonged period of stress due to social isolation, illness, death, and other major life disruptions. Neural reward sensitivity, essential for healthy functioning, may become reduced under major naturalistic stressors, though few studies have examined this. The present study sought to test whether neural responses to rewards were significantly blunted by the stress of the pandemic.

METHODS

We compared 2 groups of young adult participants, who completed a monetary reward task while an electroencephalogram was recorded, at 2 time points, 1 to 3 years apart. Our measure of reward sensitivity was the reward positivity (RewP), a neural marker enhanced to gain relative to loss feedback. The magnitude of the RewP is sensitive to stress exposure and can prospectively predict depression. The pre-pandemic group (n = 41) completed both time points before the pandemic, while the pandemic group (n = 39) completed the baseline visit before the pandemic and the follow-up visit during its second year.

RESULTS

The pandemic group reported having experienced significant stressors over the course of the pandemic. We did not observe a significant decrease in the RewP from baseline to follow-up in the pre-pandemic group. In contrast, in the pandemic group, the RewP was significantly blunted at the follow-up visit to the extent that it no longer distinguished gain from loss feedback.

CONCLUSIONS

These results suggest that prolonged naturalistic stressors can result in adaptations in neural responses to rewards. Our findings also highlight a possible mechanism linking stress to the development of depression.

Modeling the left digit effect in adult number line estimation

Number line estimation tasks are frequently used to study numerical cognition skills. In a typical version, the bounded number line task, target numerals must be placed on a bounded line labeled only at its endpoints (e.g., with 0 and 100). Placements by adults, while highly accurate, reveal a cyclical pattern of over- and underestimation of target numerals. The pattern suggests use of proportion judgment strategies and is well-captured by cyclical power models. Another systematic number line bias that has recently been observed, but has not yet been considered in modeling efforts, is the left digit effect. Numerals with different leftmost digits (e.g., 39 and 41) are placed farther apart on a line than is warranted. In the current study (N = 60), adult estimates were obtained for all numerals on a 0-100 number line estimation task, and fit of the standard cyclical power model was compared with two modified versions of the model. One modified version included a parameter that underweights the rightward digit's place value (e.g., the ones digit here), and the other used the same parameter to underweight all digits' place values. We found that both modifications provided a considerably better fit for individual and median data than the standard model, and we discuss their relative merits and cognitive interpretations. The data and models suggest how a left digit bias might impact estimates across the number line.

Consensus Goals in the Field of Visual Metacognition

Despite the tangible progress in psychological and cognitive sciences over the last several years, these disciplines still trail other more mature sciences in identifying the most important questions that need to be solved. Reaching such consensus could lead to greater synergy across different laboratories, faster progress, and increased focus on solving important problems rather than pursuing isolated, niche efforts. Here, 26 researchers from the field of visual metacognition reached consensus on four long-term and two medium-term common goals. We describe the process that we followed, the goals themselves, and our plans for accomplishing these goals. If this effort proves successful within the next few years, such consensus building around common goals could be adopted more widely in psychological science.

Confidence at the limits of human nested cognition

Metacognition is the ability to weigh the quality of our own cognition, such as the confidence that our perceptual decisions are correct. Here we ask whether metacognitive performance can itself be evaluated or else metacognition is the ultimate reflective human faculty. Building upon a classic visual perception task, we show that human observers are able to produce nested, above-chance judgements on the quality of their decisions at least up to the fourth order (i.e. meta-meta-meta-cognition). A computational model can account for this nested cognitive ability if evidence has a high-resolution representation, and if there are two kinds of noise, including recursive evidence degradation. The existence of fourth-order sensitivity suggests that the neural mechanisms responsible for second-order metacognition can be flexibly generalized to evaluate any cognitive process, including metacognitive evaluations themselves. We define the theoretical and practical limits of nested cognition and discuss how this approach paves the way for a better understanding of human self-regulation.

Foundations of intuitive power analyses in children and adults

Decades of research indicate that some of the epistemic practices that support scientific enquiry emerge as part of intuitive reasoning in early childhood. Here, we ask whether adults and young children can use intuitive statistical reasoning and metacognitive strategies to estimate how much information they might need to solve different discrimination problems, suggesting that they have some of the foundations for 'intuitive power analyses'. Across five experiments, both adults (N = 290) and children (N = 48, 6-8 years) were able to precisely represent the relative difficulty of discriminating populations and recognized that larger samples were required for populations with greater overlap. Participants were sensitive to the cost of sampling, as well as the perceptual nature of the stimuli. These findings indicate that both young children and adults metacognitively represent their own ability to make discriminations even in the absence of data, and can use this to guide efficient and effective exploration.

Hate crime towards minoritized groups increases as they increase in sized-based rank

People are on the move in unprecedented numbers within and between countries. How does demographic change affect local intergroup dynamics? Complementing accounts that emphasize stereotypical features of groups as determinants of their treatment, we propose the group reference dependence hypothesis: violence and negative attitudes towards each minoritized group will depend on the number and size of other minoritized groups in a community. Specifically, as groups increase or decrease in rank in terms of their size (for example, to the largest minority within a community), discriminatory behaviour and attitudes towards them should change accordingly. We test this hypothesis for hate crimes in US counties between 1990 and 2010 and attitudes in the United States and United Kingdom over the past two decades. Consistent with this prediction, we find that as Black, Hispanic/Latinx, Asian and Arab populations increase in rank relative to one another, they become more likely to be targeted with hate crimes and more negative attitudes. The rank effect holds above and beyond group size/proportion, growth rate and many other alternative explanations. This framework makes predictions about how demographic shifts may affect coalitional structures in the coming years and helps explain previous findings in the literature. Our results also indicate that attitudes and behaviours towards social categories are not intransigent or driven only by features associated with those groups, such as stereotypes.

Perception is rich and probabilistic

When we see a stimulus, e.g. a star-shaped object, our intuition is that we should perceive a single, coherent percept (even if it is inaccurate). But the neural processes that support perception are complex and probabilistic. Simple lines cause orientation-selective neurons across a population to fire in a probabilistic-like manner. Does probabilistic neural firing lead to non-probabilistic perception, or are the representations behind perception richer and more complex than intuition would suggest? To test this, we briefly presented a complex shape and had participants report the correct shape from a set of options. Rather than reporting a single value, we used a paradigm designed to encourage to directly report a representation over shape space—participants placed a series of Gaussian bets. We found that participants could report more than point-estimates of shape. The spread of responses was correlated with accuracy, suggesting that participants can convey a notion of relative imprecision. Critically, as participants placed more bets, the mean of responses show increased precision. The later bets were systematically biased towards the target rather than haphazardly placed around bet 1. These findings strongly indicate that participants were aware of more than just a point-estimate; Perceptual representations are rich and likely probabilistic.

Suprathreshold perceptual decisions constrain models of confidence

Perceptual confidence is an important internal signal about the certainty of our decisions and there is a substantial debate on how it is computed. We highlight three confidence metric types from the literature: observers either use 1) the full probability distribution to compute probability correct (Probability metrics), 2) point estimates from the perceptual decision process to estimate uncertainty (Evidence-Strength metrics), or 3) heuristic confidence from stimulus-based cues to uncertainty (Heuristic metrics). These metrics are rarely tested against one another, so we examined models of all three types on a suprathreshold spatial discrimination task. Observers were shown a cloud of dots sampled from a dot generating distribution and judged if the mean of the distribution was left or right of centre. In addition to varying the horizontal position of the mean, there were two sensory uncertainty manipulations: the number of dots sampled and the spread of the generating distribution. After every two perceptual decisions, observers made a confidence forced-choice judgement whether they were more confident in the first or second decision. Model results showed that the majority of observers were best-fit by either: 1) the Heuristic model, which used dot cloud position, spread, and number of dots as cues; or 2) an Evidence-Strength model, which computed the distance between the sensory measurement and discrimination criterion, scaled according to sensory uncertainty. An accidental repetition of some sessions also allowed for the measurement of confidence agreement for identical pairs of stimuli. This N-pass analysis revealed that human observers were more consistent than their best-fitting model would predict, indicating there are still aspects of confidence that are not captured by our modelling. As such, we propose confidence agreement as a useful technique for computational studies of confidence. Taken together, these findings highlight the idiosyncratic nature of confidence computations for complex decision contexts and the need to consider different potential metrics and transformations in the confidence computation.

The feeling of confidence in what we perceive can influence our future behaviour and learning. Understanding how the brain computes confidence is an important goal of researchers. As such, researchers have identified a host of potential models. Yet, rarely are a wide range of models tested against each other to find those that best predict choice behaviour. Our study had human participants compare their confidence for pairs of easy perceptual decisions, reporting if they had higher confidence in the first or second decision. We tested twelve models, covering all three types of models proposed in previous studies, finding strong support for two models. The winning Heuristic model combines all three factors affecting choice uncertainty with an idiosyncratic weighting to compute confidence. The other winning model uses a transformation where the strength of the sensory signal is scaled according to sensory uncertainty. We also assessed the agreement of confidence reports in identical decision scenarios. Humans had higher agreement than almost all model predictions. We propose using confidence agreement intentionally as a second performance benchmark of model fit.

Becoming ‘Homo Economicus’ as Learned Behavior among Numerate Greek University Students

In this study, we use experimental methods to probe how far individuals depart from choices consistent with “Rational Economic Man” and whether these departures are associated with financial and numeric literature on the one hand, and, more fundamentally, with impulsive or analytical thinking—i.e., with cognitive reflection. We examine a purposely biased sample of Greek undergraduates enrolled in a course heavy on statistics and probability who participated in a battery of tests. Specifically, we use the Cognitive Reflection Test (CRT) jointly with numeric and financial literacy tools to understand how “irrational choices” result. Despite the expected bias, responders with lower CRT are more likely to be susceptible to behavioral biases, even when controlling for numeracy and financial literacy. In agreement with other studies, gender is associated with significance differences, which operate both independently and through the mediation of CRT.

Summary accuracy feedback and the left digit effect in number line estimation

A robust left digit effect arises in number line estimation such that adults' estimates for numerals with different hundreds place digits but nearly identical magnitudes are systematically different from one another (e.g., 299 is placed too far to the left of 302). In two experiments, we investigate whether brief feedback interventions designed to increase task effort can reduce or eliminate the left digit effect in a self-paced 0-1,000 number line estimation task. Participants were assigned to complete three blocks of 120 trials each where the middle block contained feedback or no feedback. Feedback was in the form of summary accuracy scores (Experiment 1; N = 153) or competitive (summary) accuracy scores (Experiment 2; N = 145). In both experiments, planned analyses revealed large left digit effects in all blocks regardless of feedback condition. Feedback did not lead to a reduction in the left digit effect in either experiment, but improvements in overall accuracy were observed. We conclude that there are no changes in the left digit effect resulting from either summary accuracy feedback or competitive accuracy feedback. Also reported are exploratory analyses of trial characteristics (e.g., whether 299 is presented before or after 302) and the left digit effect.

Causal Support: Modeling Causal Inferences with Visualizations

Analysts often make visual causal inferences about possible data-generating models. However, visual analytics (VA) software tends to leave these models implicit in the mind of the analyst, which casts doubt on the statistical validity of informal visual "insights". We formally evaluate the quality of causal inferences from visualizations by adopting causal support-a Bayesian cognition model that learns the probability of alternative causal explanations given some data-as a normative benchmark for causal inferences. We contribute two experiments assessing how well crowdworkers can detect (1) a treatment effect and (2) a confounding relationship. We find that chart users' causal inferences tend to be insensitive to sample size such that they deviate from our normative benchmark. While interactively cross-filtering data in visualizations can improve sensitivity, on average users do not perform reliably better with common visualizations than they do with textual contingency tables. These experiments demonstrate the utility of causal support as an evaluation framework for inferences in VA and point to opportunities to make analysts' mental models more explicit in VA software.

Visualization Equilibrium

In many real-world strategic settings, people use information displays to make decisions. In these settings, an information provider chooses which information to provide to strategic agents and how to present it, and agents formulate a best response based on the information and their anticipation of how others will behave. We contribute the results of a controlled online experiment to examine how the provision and presentation of information impacts people's decisions in a congestion game. Our experiment compares how different visualization approaches for displaying this information, including bar charts and hypothetical outcome plots, and different information conditions, including where the visualized information is private versus public (i.e., available to all agents), affect decision making and welfare. We characterize the effects of visualization anticipation, referring to changes to behavior when an agent goes from alone having access to a visualization to knowing that others also have access to the visualization to guide their decisions. We also empirically identify the visualization equilibrium, i.e., the visualization for which the visualized outcome of agents' decisions matches the realized decisions of the agents who view it. We reflect on the implications of visualization equilibria and visualization anticipation for designing information displays for real-world strategic settings.

Additively Combining Utilities and Beliefs: Research Gaps and Algorithmic Developments

Value-based decision making in complex environments, such as those with uncertain and volatile mapping of reward probabilities onto options, may engender computational strategies that are not necessarily optimal in terms of normative frameworks but may ensure effective learning and behavioral flexibility in conditions of limited neural computational resources. In this article, we review a suboptimal strategy - additively combining reward magnitude and reward probability attributes of options for value-based decision making. In addition, we present computational intricacies of a recently developed model (named MIX model) representing an algorithmic implementation of the additive strategy in sequential decision-making with two options. We also discuss its opportunities; and conceptual, inferential, and generalization issues. Furthermore, we suggest future studies that will reveal the potential and serve the further development of the MIX model as a general model of value-based choice making.

Biased evaluations emerge from inferring hidden causes

How do we evaluate a group of people after a few negative experiences with some members but mostly positive experiences otherwise? How do rare experiences influence our overall impression? We show that rare events may be overweighted due to normative inference of the hidden causes that are believed to generate the observed events. We propose a Bayesian inference model that organizes environmental statistics by combining similar events and separating outlying observations. Relying on the model's inferred latent causes for group evaluation overweights rare or variable events. We tested the model's predictions in eight experiments where participants observed a sequence of social or non-social behaviours and estimated their average. As predicted, estimates were biased toward sparse events when estimating after seeing all observations, but not when tracking a summary value as observations accrued. Our results suggest that biases in evaluation may arise from inferring the hidden causes of group members' behaviours.

Can Visualization Alleviate Dichotomous Thinking? Effects of Visual Representations on the Cliff Effect

Common reporting styles for statistical results in scientific articles, such as p-values and confidence intervals (CI), have been reported to be prone to dichotomous interpretations, especially with respect to the null hypothesis significance testing framework. For example when the p-value is small enough or the CIs of the mean effects of a studied drug and a placebo are not overlapping, scientists tend to claim significant differences while often disregarding the magnitudes and absolute differences in the effect sizes. This type of reasoning has been shown to be potentially harmful to science. Techniques relying on the visual estimation of the strength of evidence have been recommended to reduce such dichotomous interpretations but their effectiveness has also been challenged. We ran two experiments on researchers with expertise in statistical analysis to compare several alternative representations of confidence intervals and used Bayesian multilevel models to estimate the effects of the representation styles on differences in researchers' subjective confidence in the results. We also asked the respondents' opinions and preferences in representation styles. Our results suggest that adding visual information to classic CI representation can decrease the tendency towards dichotomous interpretations - measured as the 'cliff effect': the sudden drop in confidence around p-value 0.05 - compared with classic CI visualization and textual representation of the CI with p-values. All data and analyses are publicly available at https://github.com/helske/statvis.

Model-Based Wisdom of the Crowd for Sequential Decision-Making Tasks

We study the wisdom of the crowd in three sequential decision-making tasks: the Balloon Analogue Risk Task (BART), optimal stopping problems, and bandit problems. We consider a behavior-based approach, using majority decisions to determine crowd behavior and show that this approach performs poorly in the BART and bandit tasks. The key problem is that the crowd becomes progressively more extreme as the decision sequence progresses, because the diversity of opinion that underlies the wisdom of the crowd is lost. We also consider model-based approaches to each task. This involves inferring cognitive models for each individual based on their observed behavior, and using these models to predict what each individual would do in any possible task situation. We show that this approach performs robustly well for all three tasks and has the additional advantage of being able to generalize to new problems for which there are no behavioral data. We discuss potential applications of the model-based approach to real-world sequential decision problems and discuss how our approach contributes to the understanding of collective intelligence.

Judgment errors in naturalistic numerical estimation

People estimate numerical quantities (such as the calories of foods) on a day-to-day basis. Although these estimates influence behavior and determine wellbeing, they are prone to two important types of errors. Scaling errors occur when people make mistakes reporting their beliefs about a particular numerical quantity (e.g. by inflating small numbers). Belief errors occur when people make mistakes using their knowledge of the judgment target to form their beliefs about the numerical quantity (e.g. by overweighting certain cues). In this paper, we quantitatively model numerical estimates, and in turn, scaling and belief errors, in everyday judgment tasks. Our approach is unique in using insights from semantic memory research to specify knowledge for naturalistic judgment targets, allowing our models to formally describe nuanced errors in belief not considered in prior research. In Studies 1 and 2, we find that belief error models predict participant estimates and errors with very high out-of-sample accuracy rates, significantly outperforming the predictions of scaling error models. In fact, the best-fitting belief error models can closely mimic the inverse-S shaped patterns captured by scaling error models, suggesting that the types of responses previously attributed to scaling errors can be seen as errors of belief. In Studies 3 to 8, we find that belief error models are also able to predict people's responses in semantic judgment, free association, and verbal protocol tasks related to numerical judgment, and thus provide a good account of the cognitive underpinnings of judgment.

MiR-9-5p Regulates Genes Linked to Cerebral Calcification in the Osteogenic Differentiation Model and Induces Generalized Alteration in the Ion Channels

MicroRNA-9 (miR-9) modulates gene expression and demonstrates high structural conservation and wide expression in the central nervous system. Bioinformatics analysis predicts almost 100 ion channels, membrane transporters and receptors, including genes linked to primary familial brain calcification (PFBC), as possible miR-9-5p targets. PFBC is a neurodegenerative disorder, characterized by bilateral and symmetrical calcifications in the brain, associated with motor and behavioral disturbances. In this work, we seek to study the influence of miR-9-5p in regulating genes involved in PFBC, in an osteogenic differentiation model with SaOs-2 cells. During the induced calcification process, solute carrier family 20 member 2 (SLC20A2) and platelet-derived growth factor receptor beta (PDGFRB) were downregulated, while platelet-derived growth factor beta (PDGFB) showed no significant changes. Significantly decreased levels of SLC20A2 and PDGFRB were caused by the presence of miR-9-5p, while PDGFB showed no regulation. We confirmed the findings using an miR-9-5p inhibitor and also probed the cells in electrophysiological analysis to assess whether such microRNA might affect a broader range of ion channels, membrane transporters and receptors. Our electrophysiological data show that an increase of the miR-9-5p in SaOs-2 cells decreased the density and amplitude of the output ionic currents, indicating that it may influence the activity, and perhaps the expression, of some ionic channels. Additional investigations should determine whether such an effect is specific to miR-9-5p, and whether it could be used, together with the miR-9-5p inhibitor, as a therapeutic or diagnostic tool.

Individual differences in the perception of probability

In recent studies of humans estimating non-stationary probabilities, estimates appear to be unbiased on average, across the full range of probability values to be estimated. This finding is surprising given that experiments measuring probability estimation in other contexts have often identified conservatism: individuals tend to overestimate low probability events and underestimate high probability events. In other contexts, repulsive biases have also been documented, with individuals producing judgments that tend toward extreme values instead. Using extensive data from a probability estimation task that produces unbiased performance on average, we find substantial biases at the individual level; we document the coexistence of both conservative and repulsive biases in the same experimental context. Individual biases persist despite extensive experience with the task, and are also correlated with other behavioral differences, such as individual variation in response speed and adjustment rates. We conclude that the rich computational demands of our task give rise to a variety of behavioral patterns, and that the apparent unbiasedness of the pooled data is an artifact of the aggregation of heterogeneous biases.

Visual Reasoning Strategies for Effect Size Judgments and Decisions

Uncertainty visualizations often emphasize point estimates to support magnitude estimates or decisions through visual comparison. However, when design choices emphasize means, users may overlook uncertainty information and misinterpret visual distance as a proxy for effect size. We present findings from a mixed design experiment on Mechanical Turk which tests eight uncertainty visualization designs: 95% containment intervals, hypothetical outcome plots, densities, and quantile dotplots, each with and without means added. We find that adding means to uncertainty visualizations has small biasing effects on both magnitude estimation and decision-making, consistent with discounting uncertainty. We also see that visualization designs that support the least biased effect size estimation do not support the best decision-making, suggesting that a chart user's sense of effect size may not necessarily be identical when they use the same information for different tasks. In a qualitative analysis of users' strategy descriptions, we find that many users switch strategies and do not employ an optimal strategy when one exists. Uncertainty visualizations which are optimally designed in theory may not be the most effective in practice because of the ways that users satisfice with heuristics, suggesting opportunities to better understand visualization effectiveness by modeling sets of potential strategies.

Discrete confidence levels revealed by sequential decisions

Humans can meaningfully express their confidence about uncertain events. Normatively, these beliefs should correspond to Bayesian probabilities. However, it is unclear whether the normative theory provides an accurate description of the human sense of confidence, partly because the self-report measures used in most studies hinder quantitative comparison with normative predictions. To measure confidence objectively, we developed a dual-decision task in which the correctness of a first decision determines the correct answer of a second decision, thus mimicking real-life situations in which confidence guides future choices. While participants were able to use confidence to improve performance, they fell short of the ideal Bayesian strategy. Instead, behaviour was better explained by a model with a few discrete confidence levels. These findings question the descriptive validity of normative accounts, and suggest that confidence judgments might be based on point estimates of the relevant variables, rather than on their full probability distributions.

The bounded rationality of probability distortion

In decision making under risk (DMR) participants' choices are based on probability values systematically different from those that are objectively correct. Similar systematic distortions are found in tasks involving relative frequency judgments (JRF). These distortions limit performance in a wide variety of tasks and an evident question is, Why do we systematically fail in our use of probability and relative frequency information? We propose a bounded log-odds model (BLO) of probability and relative frequency distortion based on three assumptions: 1) log-odds: probability and relative frequency are mapped to an internal log-odds scale, 2) boundedness: the range of representations of probability and relative frequency are bounded and the bounds change dynamically with task, and 3) variance compensation: the mapping compensates in part for uncertainty in probability and relative frequency values. We compared human performance in both DMR and JRF tasks to the predictions of the BLO model as well as 11 alternative models, each missing one or more of the underlying BLO assumptions (factorial model comparison). The BLO model and its assumptions proved to be superior to any of the alternatives. In a separate analysis, we found that BLO accounts for individual participants' data better than any previous model in the DMR literature. We also found that, subject to the boundedness limitation, participants' choice of distortion approximately maximized the mutual information between objective task-relevant values and internal values, a form of bounded rationality.

The nature of metacognitive inefficiency in perceptual decision making

Humans have the metacognitive ability to judge the accuracy of their own decisions via confidence ratings. A substantial body of research has demonstrated that human metacognition is fallible but it remains unclear how metacognitive inefficiency should be incorporated into a mechanistic model of confidence generation. Here we show that, contrary to what is typically assumed, metacognitive inefficiency depends on the level of confidence. We found that, across 5 different data sets and 4 different measures of metacognition, metacognitive ability decreased with higher confidence ratings. To understand the nature of this effect, we collected a large dataset of 20 subjects completing 2,800 trials each and providing confidence ratings on a continuous scale. The results demonstrated a robustly nonlinear zROC curve with downward curvature, despite a decades-old assumption of linearity. This pattern of results was reproduced by a new mechanistic model of confidence generation, which assumes the existence of lognormally distributed metacognitive noise. The model outperformed competing models either lacking metacognitive noise altogether or featuring Gaussian metacognitive noise. Further, the model could generate a measure of metacognitive ability which was independent of confidence levels. These findings establish an empirically validated model of confidence generation, have significant implications about measures of metacognitive ability, and begin to reveal the underlying nature of metacognitive inefficiency. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Healthcare Professionals Risk Assessments for Alert Overrides in High-Risk IV Infusions Using Simulated Scenarios

This study aimed to use healthcare professionals' assessments to calculate expected risk of intravenous (IV) infusion harm for simulated high-risk medications that exceed soft limits and to investigate the impact of relevant risk factors. We designed 30 infusion scenarios for four high-risk medications, propofol, morphine, insulin, and heparin, infused in adult intensive care unit (AICU) and adult medical and surgical care unit (AMSU). A total of 20 pharmacists and 5 nurses provided their assessed expected risk of harm in each scenario. Descriptive statistics, analysis of variance with least square mean, and post hoc test were conducted to test the effects of field limit type, soft (SoftMax), and hard maximum drug limit types (HardMax), and care area-medication combination on risk of harm. The results showed that overdosing scenarios with continuous and bolus dose limit types were assessed with significantly higher risks than those of bolus dose rate type. An overdose infusion in AICU over a large SoftMax was assessed to be of higher risk than over a small one, but not in AMSU. For overdose infusions with three levels of drug amount, greater drug amount in AICU and AMSU was assessed to have higher risk, except insignificant risk difference between the infusions with higher and moderate drug amount in AMSU. This study obtained expected risk for simulated high-risk IV infusions and found that different field limit and SoftMax types can affect expected risk based on healthcare professionals' perspectives. The findings will be regarded as benchmarks for validating risk quantification models in future research.

Resource-rational analysis versus resource-rational humans

Lieder and Griffiths advocate for resource-rational analysis as a methodological device employed by the experimenter. However, at times this methodological device appears to morph into the substantive claim that humans are actually resource-rational. Such morphing is problematic; the methodological approach used by the experimenter and claims about the nature of human behavior ought to be kept completely separate.

Intuitive symbolic magnitude judgments and decision making under risk in adults

Performance on an intuitive symbolic number skills task-namely the number line estimation task-has previously been found to predict value function curvature in decision making under risk, using a cumulative prospect theory (CPT) model. However there has been no evidence of a similar relationship with the probability weighting function. This is surprising given that both number line estimation and probability weighting can be construed as involving proportion judgment, that is, involving estimating a number on a bounded scale based on its proportional relationship to the whole. In the present work, we re-evaluated the relationship between number line estimation and probability weighting through the lens of proportion judgment. Using a CPT model with a two-parameter probability weighting function, we found a double dissociation: number line estimation bias predicted probability weighting curvature while performance on a different number skills task, number comparison, predicted probability weighting elevation. Interestingly, while degree of bias was correlated across tasks, the direction of bias was not. The findings provide support for proportion judgment as a plausible account of the shape of the probability weighting function, and suggest directions for future work.

Why are older adults victims of fraud? Current knowledge and prospects regarding older adults' vulnerability to fraud

Older adults are disproportionately targeted by various kinds of fraud, which result in irreversible economic losses and great psychological distress. Over the past years, researchers have conducted systematic research on the prevalence, under-reporting, and research methods of fraud victimization in older adults. Research paradigms regarding fraud victimization among older adults have mainly included cognitive, emotion regulation and motivation, and comprehensive paradigms. Factors shown to influence fraud victimization among older adults include cognitive decline, emotional regulation and motivational changes, their overly trusting nature, psychological vulnerability, social isolation, risk-taking, and a lack of knowledge and information regarding fraud prevention. Based on a review of the literature, future research can benefit from constructing a comprehensive fraud victimization theory, improving research methods, extending existing research, exploring physiological mechanisms of elderly fraud, and strengthening prevention and intervention efforts.

Probability range and probability distortion in a gambling task

In decision making under risk, adults tend to overestimate small and underestimate large probabilities (Tversky & Kahneman, 1992). This inverse S-shaped distortion pattern is similar to that observed in a wide variety of proportion judgment tasks (see Hollands & Dyre, 2000, for review). In proportion judgment tasks, distortion patterns tend not to be fixed but rather to depend on the reference points to which the targets are compared. Here, we tested the novel hypothesis that probability distortion in decision making under risk might also be influenced by reference points-in this case, references implied by the probability range. Adult participants were assigned to either a full-range (probabilities from 0-100%), upper-range (50-100%), or lower-range (0-50%) condition, where they indicated certainty equivalents for 176 hypothetical monetary gambles (e.g., "a 50% chance of $100, otherwise $0"). Using a modified cumulative prospect theory model, we found only minimal differences in probability distortion as a function of condition, suggesting no differences in use of reference points by condition, and broadly demonstrating the robustness of distortion pattern across contexts. However, we also observed deviations from the curve across all conditions that warrant further research.

Human representation of multimodal distributions as clusters of samples

Behavioral and neuroimaging evidence shows that human decisions are sensitive to the statistical regularities (mean, variance, skewness, etc.) of reward distributions. However, it is unclear what representations human observers form to approximate reward distributions, or probability distributions in general. When the possible values of a probability distribution are numerous, it is cognitively costly and perhaps unrealistic to maintain in mind the probability of each possible value. Here we propose a Clusters of Samples (CoS) representation model: The samples of the to-be-represented distribution are classified into a small number of clusters and only the centroids and relative weights of the clusters are retained for future use. We tested the behavioral relevance of CoS in four experiments. On each trial, human subjects reported the mean and mode of a sequentially presented multimodal distribution of spatial positions or orientations. By varying the global and local features of the distributions, we observed systematic errors in the reported mean and mode. We found that our CoS representation of probability distributions outperformed alternative models in accounting for subjects’ response patterns. The ostensible influence of positive/negative skewness on the over/under estimation of the reported mean, analogous to the “skewness preference” phenomenon in decisions, could be well explained by models based on CoS.

Life is full of uncertainties: An action may yield multiple possible consequences and a percept may imply multiple possible causes. To survive, humans and animals must compensate for the uncertainty in the environment and in their own perceptual and motor systems. However, how humans represent probability distributions to fulfill probabilistic computations for perception and action remains elusive. The number of possible values in a distribution is vast and grows exponentially with the dimension of the distribution. It would be costly, if not impossible, to maintain the probability of each possible value. Here we propose a sparse representation of probability distributions, which can reduce an arbitrary distribution to a small set of coefficients while still keeping important global and local features of the original distribution. Our experiments provide preliminary evidence for the use of such representations in human cognition.

Segmented poly(A) tails significantly reduce recombination of plasmid DNA without affecting mRNA translation efficiency or half-life

Extensive research in the past decade has brought mRNA closer to the clinical realization of its therapeutic potential. One common structural feature for all cellular messenger RNAs is a poly(A) tail, which can either be brought in cotranscriptionally via the DNA template (plasmid- or PCR-based) or added to the mRNA in a post-transcriptional enzymatic process. Plasmids containing poly(A) regions recombine in E. coli, resulting in extensive shortening of the poly(A) tail. Using a segmented poly(A) approach, we could significantly reduce recombination of plasmids in E. coli without any negative effect on mRNA half-life and protein expression. This effect was independent of the coding sequence. A segmented poly(A) tail is characterized in that it consists of at least two A-containing elements, each defined as a nucleotide sequence consisting of 40-60 adenosines, separated by a spacer element of different length. Furthermore, reducing the spacer length between the poly(A) segments resulted in higher translation efficiencies compared to homogeneous poly(A) tail and reduced recombination (depending upon the choice of spacer nucleotide). Our results demonstrate the superior potential of segmented poly(A) tails compared to the conventionally used homogeneous poly(A) tails with respect to recombination of the plasmids and the resulting mRNA performance (half-life and translational efficiency).

Prefrontal mechanisms combining rewards and beliefs in human decision-making

In uncertain and changing environments, optimal decision-making requires integrating reward expectations with probabilistic beliefs about reward contingencies. Little is known, however, about how the prefrontal cortex (PFC), which subserves decision-making, combines these quantities. Here, using computational modelling and neuroimaging, we show that the ventromedial PFC encodes both reward expectations and proper beliefs about reward contingencies, while the dorsomedial PFC combines these quantities and guides choices that are at variance with those predicted by optimal decision theory: instead of integrating reward expectations with beliefs, the dorsomedial PFC built context-dependent reward expectations commensurable to beliefs and used these quantities as two concurrent appetitive components, driving choices. This neural mechanism accounts for well-known risk aversion effects in human decision-making. The results reveal that the irrationality of human choices commonly theorized as deriving from optimal computations over false beliefs, actually stems from suboptimal neural heuristics over rational beliefs about reward contingencies.

Optimal decision-making requires integrating expectations about rewards with beliefs about reward contingencies. Here, the authors show that these aspects of reward are encoded in the ventromedial prefrontal cortex then combined in the dorsomedial prefrontal cortex, a process that guides choice biases characteristic of human decision-making.

Interaction Effects of Religiosity Level on the Relationship between Religion and Willingness to Donate Organs

This study aims to investigate the interaction effect of religiosity level on the relationship between religion and willingness to donate organs. Prior studies have suggested that a high level of religiosity indicates a high level of willingness to donate organs. However, these previous works ignore the interaction effect of the level of religiosity and the doctrinal characteristics of each religion regarding one’s own body preservation. Organ donation is an act of transplanting part of one’s own body after death to another person and is influenced by the viewpoint of the post-mortem world and the attitude toward the preservation of the body. Therefore, this study analyzes the effects of religious characteristics and belief levels on the relationship between religion and organ donation. Results show that Christianity, such as Catholicism and Protestantism, positively affects the willingness to donate organs as compared with Buddhism. Religiosity level also exerts an interaction effect that strengthens the relationship between Christianity and willingness to donate organs.

Bias and ignorance in demographic perception

When it comes to knowledge of demographic facts, misinformation appears to be the norm. Americans massively overestimate the proportions of their fellow citizens who are immigrants, Muslim, LGBTQ, and Latino, but underestimate those who are White or Christian. Previous explanations of these estimation errors have invoked topic-specific mechanisms such as xenophobia or media bias. We reconsidered this pattern of errors in the light of more than 30 years of research on the psychological processes involved in proportion estimation and decision-making under uncertainty. In two publicly available datasets featuring demographic estimates from 14 countries, we found that proportion estimates of national demographics correspond closely to what is found in laboratory studies of quantitative estimates more generally. Biases in demographic estimation, therefore, are part of a very general pattern of human psychology-independent of the particular topic or demographic under consideration-that explains most of the error in estimates of the size of politically salient populations. By situating demographic estimates within a broader understanding of general quantity estimation, these results demand reevaluation of both topic-specific misinformation about demographic facts and topic-specific explanations of demographic ignorance, such as media bias and xenophobia.

Evidence accumulation in a Laplace domain decision space

Evidence accumulation models of simple decision-making have long assumed that the brain estimates a scalar decision variable corresponding to the log-likelihood ratio of the two alternatives. Typical neural implementations of this algorithmic cognitive model assume that large numbers of neurons are each noisy exemplars of the scalar decision variable. Here we propose a neural implementation of the diffusion model in which many neurons construct and maintain the Laplace transform of the distance to each of the decision bounds. As in classic findings from brain regions including LIP, the firing rate of neurons coding for the Laplace transform of net accumulated evidence grows to a bound during random dot motion tasks. However, rather than noisy exemplars of a single mean value, this approach makes the novel prediction that firing rates grow to the bound exponentially; across neurons there should be a distribution of different rates. A second set of neurons records an approximate inversion of the Laplace transform; these neurons directly estimate net accumulated evidence. In analogy to time cells and place cells observed in the hippocampus and other brain regions, the neurons in this second set have receptive fields along a "decision axis." This finding is consistent with recent findings from rodent recordings. This theoretical approach places simple evidence accumulation models in the same mathematical language as recent proposals for representing time and space in cognitive models for memory.

A formal model of fuzzy-trace theory: Variations on framing effects and the Allais paradox

Fuzzy-trace theory assumes that decision-makers process qualitative "gist" representations and quantitative "verbatim" representations in parallel. We develop a lattice model of fuzzy-trace theory that explains both processes. Specifically, the model provides a novel formalization of how: 1) decision-makers encode multiple representations of options in parallel; 2) representations compete or combine so that choices often turn on the simplest representation of encoded gists; and 3) choices between representations are made based on positive vs. negative valences associated with social and moral principles stored in long-term memory (e.g., saving lives is good). The model integrates effects of individual differences in numeracy, metacognitive monitoring and editing, and sensation seeking. We conducted a systematic review of variations on framing effects and the Allais Paradox, both core phenomena of risky decision-making, and tested whether our model could predict observed choices: The model successfully predicted 82 out of 88 (93%) pairs of studies (comparing gain to loss conditions) demonstrating 16 variations on effects, theoretically critical manipulations that eliminate or exaggerate framing effects. When examining these conditions individually, the model successfully predicted 153 (90%) out of 170 eligible studies. Parameters of the model varied in theoretically meaningful ways with differences in numeracy, metacognitive monitoring, and sensation seeking, accounting for risk preferences at the group level. New experiments show similar results at the individual level. The model is also shown to be scientifically parsimonious using standard measures. Relations to current theories, such as Cumulative Prospect Theory, and potential extensions are discussed.

Context Effects in the Judgment of Visual Relative-Frequency: Trial-by-Trial Adaptation and Non-linear Sequential Effect

Humans' judgment of relative-frequency, similar to their use of probability in decision-making, is often distorted as an inverted-S-shape curve-small relative-frequency overestimated and large relative-frequency underestimated. Here we investigated how the judgment of relative-frequency, despite its natural reference points (0 and 1) and stereotyped distortion, may adapt to the environmental statistics. The task was to report the relative-frequency of black (or white) dots in a visual array of black and white dots. We found that participants' judgment was distorted in the typical inverted-S-shape, but the distortion curve was influenced by both the central tendency and spread of the distribution of objective relative-frequencies: the lower the central tendency, the higher the overall judgment (contrast effect); the higher the spread, the more curved the inverted-S-shape (curvature effect). These context effects are in the spirit of efficient coding but opposite to what would be predicted by Bayesian inference. We further modeled the context effects on the level of individual trials, through which we found not only a trial-by-trial adaptation, but also the non-linear sequential effects that were recently reported mainly in circularly distributed visual stimuli.