The autocorrelated Bayesian sampler: A rational process for probability judgments, estimates, confidence intervals, choices, confidence judgments, and response times.

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. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A unified explanation of variability and bias in human probability judgments: How computational noise explains the mean-variance signature.

Human probability judgments are both variable and subject to systematic biases. Most probability judgment models treat variability and bias separately: a deterministic model explains the origin of bias, to which a noise process is added to generate variability. But these accounts do not explain the characteristic inverse U-shaped signature linking mean and variance in probability judgments. By contrast, models based on sampling generate the mean and variance of judgments in a unified way: the variability in the response is an inevitable consequence of basing probability judgments on a small sample of remembered or simulated instances of events. We consider two recent sampling models, in which biases are explained either by the sample accumulation being further corrupted by retrieval noise (the Probability Theory + Noise account) or as a Bayesian adjustment to the uncertainty implicit in small samples (the Bayesian sampler). While the mean predictions of these accounts closely mimic one another, they differ regarding the predicted relationship between mean and variance. We show that these models can be distinguished by a novel linear regression method that analyses this crucial mean-variance signature. First, the efficacy of the method is established using model recovery, demonstrating that it more accurately recovers parameters than complex approaches. Second, the method is applied to the mean and variance of both existing and new probability judgment data, confirming that judgments are based on a small number of samples that are adjusted by a prior, as predicted by the Bayesian sampler. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Clarifying the relationship between coherence and accuracy in probability judgments.

Bayesian approaches presuppose that following the coherence conditions of probability theory makes probabilistic judgments more accurate. But other influential theories claim accurate judgments (with high "ecological rationality") do not need to be coherent. Empirical results support these latter theories, threatening Bayesian models of intelligence; and suggesting, moreover, that "heuristics and biases" research, which focuses on violations of coherence, is largely irrelevant. We carry out a higher-power experiment involving poker probability judgments (and a formally analogous urn task), with groups of poker novices, occasional poker players, and poker experts, finding a positive relationship between coherence and accuracy both between groups and across individuals. Both the positive relationship in our data, and past null results, are captured by a sample-based Bayesian approximation model, where a person's accuracy and coherence both increase with the number of samples drawn. Thus, we reconcile the theoretical link between accuracy and coherence with apparently negative empirical results.

Precise/not precise (PNP): A Brunswikian model that uses judgment error distributions to identify cognitive processes.

In 1956, Brunswik proposed a definition of what he called intuitive and analytic cognitive processes, not in terms of verbally specified properties, but operationally based on the observable error distributions. In the decades since, the diagnostic value of error distributions has generally been overlooked, arguably because of a long tradition to consider the error as exogenous (and irrelevant) to the process. Based on Brunswik's ideas, we develop the precise/not precise (PNP) model, using a mixture distribution to model the proportion of error-perturbed versus error-free executions of an algorithm, to determine if Brunswik's claims can be replicated and extended. In Experiment 1, we demonstrate that the PNP model recovers Brunswik's distinction between perceptual and conceptual tasks. In Experiment 2, we show that also in symbolic tasks that involve no perceptual noise, the PNP model identifies both types of processes based on the error distributions. In Experiment 3, we apply the PNP model to confirm the often-assumed "quasi-rational" nature of the rule-based processes involved in multiple-cue judgment. The results demonstrate that the PNP model reliably identifies the two cognitive processes proposed by Brunswik, and often recovers the parameters of the process more effectively than a standard regression model with homogeneous Gaussian error, suggesting that the standard Gaussian assumption incorrectly specifies the error distribution in many tasks. We discuss the untapped potentials of using error distributions to identify cognitive processes and how the PNP model relates to, and can enlighten, debates on intuition and analysis in dual-systems theories.

Compound risk judgment in tasks with both idiosyncratic and systematic risk: The "Robust Beauty" of additive probability integration.

In this study, we explore how people integrate risks of assets in a simulated financial market into a judgment of the conjunctive risk that all assets decrease in value, both when assets are independent and when there is a systematic risk present affecting all assets. Simulations indicate that while mental calculation according to naïve application of probability theory is best when the assets are independent, additive or exemplar-based algorithms perform better when systematic risk is high. Considering that people tend to intuitively approach compound probability tasks using additive heuristics, we expected the participants to find it easiest to master tasks with high systematic risk - the most complex tasks from the standpoint of probability theory - while they should shift to probability theory or exemplar memory with independence between the assets. The results from 3 experiments confirm that participants shift between strategies depending on the task, starting off with the default of additive integration. In contrast to results in similar multiple cue judgment tasks, there is little evidence for use of exemplar memory. The additive heuristics also appear to be surprisingly context-sensitive, with limited generalization across formally very similar tasks.