Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any claim against the existence of an algorithm, Bayesian or otherwise, is impossible to evaluate unless one specifies the information format in which it is designed to operate. The authors show that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Frequency formats correspond to the sequential way information is acquired in natural sampling, from animal foraging to neural networks. By analyzing several thousand solutions to Bayesian problems, the authors found that when information was presented in frequency formats, statistically naive participants derived up to 50 % of all inferences by Bayesian algorithms. Non-Bayesian algorithms included simple versions of Fisherian and Neyman-Pearsonian inference. Is the mind, by design, predisposed against performing Bayesian inference? The classical probabilists of the Enlightenment, including Condorcet, Poisson, and Laplace, equated probability theory with the common sense of educated people, who were known then as “hommes éclairés.” Laplace (1814/1951) declared that “the theory of probability is at bottom nothing more than good sense reduced to a calculus which evaluates that which good minds know by a sort of instinct,

Elicitation is a key task for subjectivist Bayesians. While skeptics hold that it cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subjectmatter-expert colleagues. This paper reviews the state-of-the-art, reflecting the experience of statisticians informed by the fruits of a long line of psychological research into how people represent uncertain information cognitively, and how they respond to questions about that information. In a discussion of the elicitation process, the first issue to address is what it means for an elicitation to be successful, i.e. what criteria should be employed? Our answer is that a successful elicitation faithfully represents the opinion of the person being elicited. It is not necessarily “true ” in some objectivistic sense, and cannot be judged that way. We see elicitation as simply part of the process of statistical modeling. Indeed in a hierarchical model it is ambiguous at which point the likelihood ends and the prior begins. Thus the same kinds of judgment that inform statistical modeling in general also inform elicitation of prior distributions.

This paper concerns the evaluation and combination of subjective probability estimates for categorical events. We argue that the appropriate criterion for evaluating individual and combined estimates depends on the type of uncertainty the decision maker seeks to represent, which in turn depends on his or her model of the event space. Decision makers require accurate estimates in the presence of aleatory uncertainty about exchangeable events, diagnostic estimates given epistemic uncertainty about unique events, and some combination of the two when the events are not necessarily unique, but the best equivalence class de®nition for exchangeable events is not apparent. Following a brief reveiw of the mathematical and empirical literature on combining judgments, we present an approach to the topic that derives from (1) a weak cognitive model of the individual that assumes subjective estimates are a function of underlying judgment perturbed by random error and (2) a classi®cation of judgment contexts in terms of the underlying information structure. In support of our developments, we present new analyses of two sets of subjective probability estimates, one of exchangeable and the other of unique events. As predicted, mean estimates were more accurate than the individual values in the ®rst case and more diagnostic in

Research suggests that causal judgment is influenced primarily by counterfactual or covariational reasoning. In contrast, the author of this article develops judgment dissociation theory (JDT), which predicts that these types of reasoning differ in function and can lead to divergent judgments. The actuality principle proposes that causal selections focus on antecedents that are sufficient to generate the actual outcome. The substitution principle proposes that ad hoc categorization plays a key role in counterfactual and covariational reasoning such that counterfactual selections focus on antecedents that would have been sufficient to prevent the outcome or something like it and covariational selections focus on antecedents that yield the largest increase in the probability of the outcome or something like it. The findings of 4 experiments support JDT but not the competing counterfactual and covariational accounts. If causation is the cement of the universe, as the philosopher David Hume (1740/1938) put it, then it is fair to say that causal knowledge is the cement that binds together each person’s representational universe. Causal reasoning—the process that generates this glue—confers many functional advantages. In virtually every sphere of human interest, our abilities to learn and categorize

Cosmides and Tooby (1996) increased performance using a frequency rather than probability frame on a problem known to elicit base-rate neglect. Analogously, Gigerenzer (1994) claimed that the conjunction fallacy disappears when formulated in terms of frequency rather than the more usual single-event probability. These authors conclude that a module or algorithm of mind exists that is able to compute with frequencies but not probabilities. The studies reported here found that base-rate neglect could also be reduced using a clearly stated single-event probability frame and by using a diagram that clarified the critical nested-set relations of the problem; that the frequency advantage could be eliminated in the conjunction fallacy by separating the critical statements so that their nested relation was opaque; and that the large effect of frequency framing on the two problems studied is not stable. Facilitation via frequency is a result of clarifying the probabilistic interpretation of the...

This paper explores the uncertainty aspects of human abductive reasoning. Echo, a model of abduction based on the Theory of Explanatory Coherence (Thagard, 1992), captures many aspects of human abductive reasoning, but fails to sufficiently manage the uncertainty in abduction. In particular, Echo does not handle belief acquisition and dynamic belief revision, two essential components of human abductive reasoning. We propose a modified Echo model (UEcho), in which we add a learning mechanism for belief acquisition and a dynamic processing mechanism for belief revision. To evaluate the model, we report an empirical study in which base rate learning serves as a testbed for belief acquisition and the order effect serves as a testbed for belief revision. Introduction Human beings are, as John Locke put it, most of the time condemned to live in the twilight of uncertainty rather than the midday sun of certainty. Managing uncertainty is thus fundamental to human beings at all le...

In learning problems available information is usually divided into two categories: examples of function values (or training data) and prior information (e.g. a smoothness constraint).

We develop a conceptual and formal clarification of the notion of surprise as a belief-based phenomenon by exploring a rich typology. Each kind of surprise is associated with a particular phase of the cognitive processing and involves particular kinds of epistemic representations (representations and expectations under scrutiny, implicit beliefs, presuppositions). We define two main kinds of surprise: mismatch-based surprise and astonishment. In the central part of the paper we suggest how a formal model of surprise can be integrated with a formal model of belief change. We investigate the role of surprise in triggering the process of belief reconsideration. There are a number of models of surprise developed in psychology of emotion. We provide several comparisons of our approach with those models.

ABSTRACT. Construing a collection of values of a sample statistic as a distribution is central to developing a coherent understanding of statistical inference. This paper discusses key developments that unfolded over three consecutive lessons in a classroom teaching experiment designed to support a group of high school students in developing such a construal. Instruction began by engaging students in activities that focused their attention on the variability among values of a common sample statistic. There occurred a critical shift in students ’ attention and discourse away from individual values of the statistic and toward a collection of such values as a basis for inferring the value of a population parameter. This was followed by their comparisons of such collections and by the emergence and application of a rule for deciding whether two such collections were similar. In the repeated application of their decision rule students structured these collections as distributions. We characterize aspects of these developments in relation to students’ classroom engagement, and we explore evidence in students ’ written work that points to how instruction shaped their conceptions.

This article will consider Hogarth's 1975 assessment that "man is a selective, sequential information processing system with limited capacity, . . . ill-suited for assessing probability distributions." Particular attention will be paid to when people make normatively "good" or "poor" probability assessments, what techniques are effective in eliciting "good," coherent probability assessments, and on how these ideas are relevant to the practicing Bayesian statistician. While there are situations where experts can make well-calibrated judgments, it will be argued that more research needs to be done into the effects of expertise, training, and feedback.