Recent decision-making models have explained behaviour using mental sampling mechanisms, but there is still little agreement on the specific sampling process, such as whether sampling rates match true probabilities. Here, we seek to trace the sampling process using generation tasks: in two experiments using general online samples (Ns = 52, 51), participants repeatedly produced potential outcomes from pairs of monetary gambles before choosing between them. Results found over-generation of rarer outcomes and under-generation of common outcomes overall, but not in initial responses, as well as avoidance of direct repetitions. Participants also tended to select options with higher average utility across their responses, implying generations guided choice. These findings suggest systematic biases in the information people may consider before a choice, and the influence that this can have on subsequent decisions, carrying implications for mental sampling models of this behaviour. We thus suggest explicit generation is a valuable method to access underlying choice processes, offering new assessments of existing theories of decision making.

Forecasting from a stream of past observations is a routine judgment task in organizations and markets, and a large literature holds that people systematically overreact when doing so, placing excessive weight on recent observations. Prominent models of expectation formation, grounded in mechanisms such as increased salience for recent signals and limited memory for past information, have predicted overreaction as a near-universal behavioral pattern, successfully capturing prior empirical findings. Here we identify boundary conditions on overreaction in expectation formation. Reanalyzing prior data in which participants viewed the full history of past realizations as a line graph, we confirm that while overreaction is most prevalent, it also varies systematically with task context, diminishing under high persistence and even reversing into underreaction as the process approaches a random walk. To test whether information display format shapes these patterns, we conducted two new experiments in which past realizations were presented sequentially, with only the most recent observation displayed (ruling out visual extrapolation). This design should, under either salience- or memory-based theories, elicit maximal overreaction. However, we find that participants instead exhibited reduced overreaction and, under high persistence, pronounced underreaction. These results establish information display format as a key moderator of forecast bias direction: reducing available history not only attenuates overreaction but can reverse its direction entirely, posing a novel challenge to prevailing theories of expectation formation.

People systematically deviate from rational Bayesian standards in belief updating, displaying biases such as base-rate neglect and conservatism. Two very different types of model aim to explain these biases: simple heuristics and stochastic sampling approximations of the Bayesian solution, like the Bayesian Sampler. However, neither approach alone accounts for the variety of responses. Here we explore a hybrid Heuristic-Anchored Bayesian Sampler (HABS) which integrates simple heuristics with a Bayesian sampler. In this framework, a simple heuristic provides an initial estimate, which may then be refined through a Bayesian sampling process to approximate the ideal Bayesian posterior. Behaviour thus depends on the size of the sample: if no samples are drawn, a heuristic response is produced, but adding samples will introduce noise while increasing average judgment accuracy. Analyses of data from a new experiment (N=200) and re-analysis of data from Stengård et al., 2022 revealed that, in most conditions, this integrative approach outperformed purely heuristic or purely Bayesian models in explaining how people update their beliefs in the medical diagnosis task. Our findings suggest that people flexibly combine mental shortcuts and approximate Bayesian processes, illuminating why some responses appear purely heuristic while others reflect approximate Bayesian updating.

Does the utility of an outcome influence people's assessment of risk and uncertainty? Prominent theories propose that people rely on mental simulation to evaluate probabilities and risky events, yet prior empirical findings is mixed as to whether and how utility biases this process. Across four experiments (total N=206, with Experiment 4 pre-registered), we tested this question using a random generation paradigm, in which participants mentally simulated gamble outcomes and said them out loud. Then we compared these responses with probability judgments and predictions. While we identified individual differences, the majority of participants exhibited neutrality, with no systematic impact of utility on their sampling distributions. Nevertheless, an optimism subgroup emerged, with a larger proportion of optimistic participants when the monetary context was more salient. Additionally, outcome utilities have similar effects on probability judgments, predictions, and random generation tasks, consistent with the proposal that these tasks are related to each other and may all rely on mental simulation. These findings indicate that utility does not uniformly distort mental simulation, but can do so for a stable subgroup under particular motivational contexts, and they motivate cognitive models that capture both unbiased and optimistic forms of mental sampling.

Noise in behavior is often considered a nuisance: Although the mind aims for the best possible action, it is let down by unreliability in the sensory and response systems. Researchers often represent noise as additive, Gaussian, and independent. Yet a careful look at behavioral noise reveals a rich structure that defies easy explanation. First, in both perceptual and preferential judgments sensory and response noise may potentially play only minor roles, with most noise arising in the cognitive computations. Second, the functional form of the noise is both non-Gaussian and nonindependent, with the distribution of noise being better characterized as heavy-tailed and as having substantial long-range autocorrelations. It is possible that this structure results from brains that are, for some reason, bedeviled by a fundamental design flaw, albeit one with intriguingly distinctive characteristics. Alternatively, noise might not be a bug but a feature. Specifically, we propose that the brain approximates probabilistic inference with a local sampling algorithm, one using randomness to drive its exploration of alternative hypotheses. Reframing cognition in this way explains the rich structure of noise and leads to the surprising conclusion that noise is not a symptom of cognitive malfunction but plays a central role in underpinning human intelligence.

Does the utility of an outcome influence people’s assessment of risk and uncertainty? Growing evidence suggests that people often rely on mental simulations to evaluate probability and risky events. However, prior experimental findings offer conflicting predictions about how utility biases this mental sampling process. Across four experiments (total N=206, with Experiment 4 pre-registered), we investigated the influence of utility using a random generation paradigm. These responses were then compared to probability judgments and predictions. While we identified individual differences, the majority of participants exhibited neutrality, with no systematic impact of utility on their sampling distributions. Nevertheless, biases emerged under specific conditions, including a preference for smaller or more probable outcomes as the starting point of simulations and optimism in single-response predictions. Additionally, we found evidence suggesting that probability judgments, predictions, and random generation tasks may rely on a shared underlying mental process. Our findings suggest that models of judgment and decision-making should account for individual differences in utility influences, particularly distinguishing between unbiased sampling and optimistic sampling—the selective over-representation of high-utility outcomes.

Recent decision making models have explained behaviour using mental sampling mechanisms, but there is still little agreement on the specific sampling process, such as whether sampling rates match true probabilities. Here, we trace the sampling process using random generation: in two experiments using general online samples (total N=103), participants repeatedly produced potential outcomes from pairs of monetary gambles before choosing between them. Results found over-generation of rarer outcomes and under-generation of common outcomes overall but not in initial responses, as well as avoidance of direct repetitions. Participants also tended to select options with higher average utility across their responses, implying generations guided choice. These findings suggest systematic biases in mental sampling that may filter through to choices, constraining models of this behaviour. We thus suggest random generation is a valuable method to access underlying choice processes, offering new assessments of existing theories of decision making.

In many real-life settings, feedback is only available for cases that decision makers accept and so may be biased toward positive events. How do people learn to distinguish good from bad alternatives from such selective feedback, and can they correct for this bias? We describe the computational problems of classification learning from biased samples and examine how exemplar and model-based methods can deal with this challenge: Model-based methods can adjust their representation of the task based on what information is available while exemplar models can impute fictive negative outcomes in missing cases to avoid positivistic biases. Importantly, these methods imply distinct assumptions about the task and reactions to missing feedback, which can be assessed empirically. In three experiments, we test whether participants rely on imputation or use a Bayesian model of the task to correct for selection bias. We find that many participants were best described by an exemplar model, most with imputation, but an almost equal proportion was best described by a Bayesian model. People best described by different models reacted somewhat differently to missing feedback. We also observe substantial stability in whether individuals were best described by model-based or exemplar models across tasks, though participants were more likely to use exemplar models when there was greater uncertainty about the task structure. Overall, our findings show that people deal with missing feedback in an adaptive manner by adopting diverse approaches that are partially stable and partially reflect assumptions made about the experimental context. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

Choices made in risky scenarios are considered fundamentally noisy because decisions have often been found to be inconsistent when repeated. Past measures of noise may, however, be confounded by the use of randomized contextual factors that are known to influence choice, in particular, the order of trials. In two experiments, we control trial order to test the extent to which inconsistent choice is attributable to changes in experimental context. Both tasks find strong evidence that trial order has no effect on choice consistency, indicating such experimental factors have little influence on behavior compared with internal noise. Choices also showed an increase in consistency across multiple repetitions, suggesting a fall in noise with experience, but this increase was not associated with any improvement in performance, with choices showing no greater adherence to either expected value or expected utility across repetitions. Instead, choices increasingly adhered to simplistic heuristic decision rules, possibly indicating greater reliance on such strategies as the tasks progressed. These results carry implications for a number of decision-making theories, including true-and-error models, rank-based methods, and strategy shift approaches.

Repeated forecasts of changing values are a key aspect of many everyday tasks, from predicting the weather to financial markets. A particularly simple and informative instance of such fluctuating values are random walks: sequences in which each point is a random movement from only its preceding value, unaffected by any previous points. Moreover, random walks often yield basic rational forecasting solutions in which predictions of new values should repeat the most recent value, and hence replicate the properties of the original series. In previous experiments, however, we have found that human forecasters do not adhere to this standard, showing systematic deviations from the properties of a random walk such as excessive volatility and extreme movements between subsequent predictions. We suggest that such deviations reflect general statistical signatures of human cognition displayed across multiple tasks, offering a window into underlying cognitive mechanisms. Using these deviations as new criteria, we here explore several cognitive models of forecasting drawn from various approaches developed in the existing literature, including Bayesian, error-based learning, autoregressive and sampling mechanisms. These models are contrasted with human data from two experiments to determine which best accounts for the particular statistical features displayed by participants. We find support for sampling models in both aggregate and individual fits, suggesting that these variations are attributable to the use of inherently stochastic prediction systems. We thus argue that variability in predictions is primarily driven by computational noise within the decision making process, rather than "late" noise at the output stage.

Psychological variability (i.e., "noise") displays interesting structure which is hidden by the common practice of averaging over trials. Interesting noise structure, termed 'stylized facts', is observed in financial markets (i.e., behaviors from many thousands of traders). Here we investigate the parallels between psychological and financial time series. In a series of three experiments (total N = 202), we successively simplified a market-based price prediction task by first removing external information, and then removing any interaction between participants. Finally, we removed any resemblance to an asset market by asking individual participants to simply reproduce temporal intervals. All three experiments reproduced the main stylized facts found in financial markets, and the robustness of the results suggests that a common cognitive-level mechanism can produce them. We identify one potential model based on mental sampling algorithms, showing how this general-purpose model might account for behavior across these very different tasks.

Normative models of decision-making that optimally transform noisy (sensory) information into categorical decisions qualitatively mismatch human behavior. Indeed, leading computational models have only achieved high empirical corroboration by adding task-specific assumptions that deviate from normative principles. In response, we offer a Bayesian approach that implicitly produces a posterior distribution of possible answers (hypotheses) in response to sensory information. But we assume that the brain has no direct access to this posterior, but can only sample hypotheses according to their posterior probabilities. Accordingly, we argue that the primary problem of normative concern in decision-making is integrating stochastic hypotheses, rather than stochastic sensory information, to make categorical decisions. This implies that human response variability arises mainly from posterior sampling rather than sensory noise. Because human hypothesis generation is serially correlated, hypothesis samples will be autocorrelated. Guided by this new problem formulation, we develop a new process, the Autocorrelated Bayesian Sampler (ABS), which grounds autocorrelated hypothesis generation in a sophisticated sampling algorithm. The ABS provides a single mechanism that qualitatively explains many empirical effects of probability judgments, estimates, confidence intervals, choice, confidence judgments, response times, and their relationships. Our analysis demonstrates the unifying power of a perspective shift in the exploration of normative models. It also exemplifies the proposal that the "Bayesian brain" operates using samples not probabilities, and that variability in human behavior may primarily reflect computational rather than sensory noise.

People must often make inferences about, and decisions concerning, a highly complex and unpredictable world, on the basis of sparse evidence. An “ideal” normative approach to such challenges is often modeled in terms of Bayesian probabilistic inference. But for real-world problems of perception, motor control, categorization, language comprehension, or common-sense reasoning, exact probabilistic calculations are computationally intractable. Instead, we suggest that the brain solves these hard probability problems approximately, by considering one, or a few, samples from the relevant distributions. By virtue of being an approximation, the sampling approach inevitably leads to systematic biases. Thus, if we assume that the brain carries over the same sampling approach to easy probability problems, where the “ideal” solution can readily be calculated, then a brain designed for probabilistic inference should be expected to display characteristic errors. We argue that many of the “heuristics and biases” found in human judgment and decision-making research can be reinterpreted as side effects of the sampling approach to probabilistic reasoning.

In many real-life settings, feedback is only available for cases decision makers accept. The selection bias generated by such missing feedback poses problems for data-driven learning algorithms, such as exemplar based models that rely on the available data to make predictions about new cases. How can exemplar algorithms deal with such biased data? Elwin et al. (2007) argued that people augment the available data with imputed missing observations: people code rejected cases, for which no feedback is available, as if the feedback was negative. It is not intuitively obvious whether relying on such internally generated feedback is sensible or leads to bias. To examine this, we analyze how exemplar learning algorithms work when missing data is imputed. We show, using simulations, mathematical analysis, and empirical data, that imputing a fictive outcome to rejected cases (Elwin et al., 2007) is an adaptive strategy: it maximizes total expected reward. Imputation helps because it compensates for the optimistic bias exemplar models suffer from when they generalize from the available data, which is subject to a selection bias. We also show that such exemplar model with imputation can perform almost as well as the optimal Bayesian approach and can provide a simple and computationally efficient way to approximate the Bayesian approach for data with a selection bias.

The brain must make inferences about, and decisions concerning, a highly complex and unpredictable world, based on sparse evidence. An “ideal” normative approach to such challenges is often modeled in terms of Bayesian probabilistic inference. But for real-world problems of perception, motor control, categorization, language understanding, or commonsense reasoning, exact probabilistic calculations are computationally intractable. Instead, we suggest that the brain solves these hard probability problems approximately, by considering one, or a few, samples from the relevant distributions. Here we provide a gentle introduction to the various sampling algorithms that have been considered as the approximation used by the brain. We broadly summarize these algorithms according to their level of knowledge and their assumptions regarding the target distribution, noting their strengths and weaknesses, their previous applications to behavioural phenomena, as well as their psychological plausibility.

Noise in behavior is often viewed as a nuisance: while the mind aims to take the best possible action, it is let down by unreliability in the sensory and motor systems. How researchers study cognition reflects this viewpoint - averaging over trials and participants in order to discover the deterministic relationships between experimental manipulations and their behavioral consequences, with noise represented as additive, often Gaussian, and independent. Yet a careful look at behavioral noise reveals rich structure that defies easy explanation. First, both perceptual and preferential judgments show that sensory and motor noise may only play minor roles, with most noise arising in the cognitive computations. Second, the functional form of the noise is both non-Gaussian and non-independent, with the distribution of noise being better characterized as heavy-tailed and as having substantial long-range autocorrelations. It is possible that this structure results from brains that are, for some reason, bedeviled by a fundamental design flaw, albeit one with intriguingly distinctive characteristics. But alternatively, noise might not be a bug, but a feature: indeed, we suggest that noise is fundamental to how cognition works. Specifically, we propose that the brain approximates probabilistic inference with a local sampling algorithm, one that uses randomness to drive its exploration of alternative hypotheses. Reframing cognition in this way explains the rich structure of noise and leads to a surprising conclusion: that noise is not a symptom of cognitive malfunction but plays a central role in underpinning human intelligence.