Two experiments investigated whether infants represent goal‐directed actions of others in a way that allows them to draw inferences to unobserved states of affairs (such as unseen goal states or occluded obstacles). We measured looking times to assess violation of infants' expectations upon perceiving either a change in the actions of computer‐animated figures or in the context of such actions. The first experiment tested whether infants would attribute a goal to an action that they had not seen completed. The second (...) experiment tested whether infants would infer from an observed action the presence of an occluded object that functions as an obstacle. The looking time patterns of 12‐month‐olds indicated that they were able to make both types of inferences, while 9‐month‐olds failed in both tasks. These results demonstrate that, by the end of the first year of life, infants use the principle of rational action not only for the interpretation and prediction of goal‐directed actions, but also for making productive inferences about unseen aspects of their context. We discuss the underlying mechanisms that may be involved in the developmental change from 9 to 12 months of age in the ability to infer hypothetical (unseen) states of affairs in teleological action representations. (shrink)

This article reviews current methods for evaluating models in the cognitive sciences, including theoretically based approaches, such as Bayes factors and minimum description length measures; simulation approaches, including model mimicry evaluations; and practical approaches, such as validation and generalization measures. This article argues that, although often useful in specific settings, most of these approaches are limited in their ability to give a general assessment of models. This article argues that hierarchical methods, generally, and hierarchical Bayesian methods, specifically, can provide a (...) more thorough evaluation of models in the cognitive sciences. This article presents two worked examples of hierarchical Bayesian analyses to demonstrate how the approach addresses key questions of descriptive adequacy, parameter interference, prediction, and generalization in principled and coherent ways. (shrink)

Inductive generalization, where people go beyond the data provided, is a basic cognitive capability, and it underpins theoretical accounts of learning, categorization, and decision making. To complete the inductive leap needed for generalization, people must make a key ‘‘sampling’’ assumption about how the available data were generated. Previous models have considered two extreme possibilities, known as strong and weak sampling. In strong sampling, data are assumed to have been deliberately generated as positive examples of a concept, whereas in weak sampling, (...) data are assumed to have been generated without any restrictions. We develop a more general account of sampling that allows for an intermediate mixture of these two extremes, and we test its usefulness. In two experiments, we show that most people complete simple one-dimensional generalization tasks in a way that is consistent with their believing in some mixture of strong and weak sampling, but that there are large individual differences in the relative emphasis different people give to each type of sampling. We also show experimentally that the relative emphasis of the mixture is influenced by the structure of the available information. We discuss the psychological meaning of mixing strong and weak sampling, and possible extensions of our modeling approach to richer problems of inductive generalization. (shrink)

The “wisdom of the crowd” phenomenon refers to the finding that the aggregate of a set of proposed solutions from a group of individuals performs better than the majority of individual solutions. Most often, wisdom of the crowd effects have been investigated for problems that require single numerical estimates. We investigate whether the effect can also be observed for problems where the answer requires the coordination of multiple pieces of information. We focus on combinatorial problems such as the planar Euclidean (...) traveling salesperson problem, minimum spanning tree problem, and a spanning tree memory task. We develop aggregation methods that combine common solution fragments into a global solution and demonstrate that these aggregate solutions outperform the majority of individual solutions. These case studies suggest that the wisdom of the crowd phenomenon might be broadly applicable to problem-solving and decision-making situations that go beyond the estimation of single numbers. (shrink)

We consider human performance on an optimal stopping problem where people are presented with a list of numbers independently chosen from a uniform distribution. People are told how many numbers are in the list, and how they were chosen. People are then shown the numbers one at a time, and are instructed to choose the maximum, subject to the constraint that they must choose a number at the time it is presented, and any choice below the maximum is incorrect. We (...) present empirical evidence that suggests people use threshold-based models to make decisions, choosing the first currently maximal number that exceeds a fixed threshold for that position in the list. We then develop a hierarchical generative account of this model family, and use Bayesian methods to learn about the parameters of the generative process, making inferences about the threshold decision models people use. We discuss the interesting aspects of human performance on the task, including the lack of learning, and the presence of large individual differences, and consider the possibility of extending the modeling framework to account for individual differences. We also use the modeling results to discuss the merits of hierarchical, generative and Bayesian models of cognitive processes more generally. (shrink)

This article demonstrates the potential of using hierarchical Bayesian methods to relate models and data in the cognitive sciences. This is done using a worked example that considers an existing model of category representation, the Varying Abstraction Model (VAM), which attempts to infer the representations people use from their behavior in category learning tasks. The VAM allows for a wide variety of category representations to be inferred, but this article shows how a hierarchical Bayesian analysis can provide a unifying explanation (...) of the representational possibilities using 2 parameters. One parameter controls the emphasis on abstraction in category representations, and the other controls the emphasis on similarity. Using 30 previously published data sets, this work shows how inferences about these parameters, and about the category representations they generate, can be used to evaluate data in terms of the ongoing exemplar versus prototype and similarity versus rules debates in the literature. Using this concrete example, this article emphasizes the advantages of hierarchical Bayesian models in converting model selection problems to parameter estimation problems, and providing one way of specifying theoretically based priors for competing models. (shrink)

Diffusion models are widely-used and successful accounts of the time course of two-choice decision making. Most diffusion models assume constant boundaries, which are the threshold levels of evidence that must be sampled from a stimulus to reach a decision. We summarize theoretical results from statistics that relate distributions of decisions and response times to diffusion models with time-varying boundaries. We then develop a computational method for finding time-varying boundaries from empirical data, and apply our new method to two problems. The (...) first problem involves finding the time-varying boundaries that make diffusion models equivalent to the alternative sequential sampling class of accumulator models. The second problem involves finding the time-varying boundaries, at the individual level, that best fit empirical data for perceptual stimuli that provide equal evidence for both decision alternatives. We discuss the theoretical and modeling implications of using time-varying boundaries in diffusion models, as well as the limitations and potential of our approach to their inference. (shrink)

We apply the “wisdom of the crowd” idea to human category learning, using a simple approach that combines people's categorization decisions by taking the majority decision. We first show that the aggregated crowd category learning behavior found by this method performs well, learning categories more quickly than most or all individuals for 28 previously collected datasets. We then extend the approach so that it does not require people to categorize every stimulus. We do this using a model‐based method that predicts (...) the categorization behavior people would produce for new stimuli, based on their behavior with observed stimuli, and uses the majority of these predicted decisions. We demonstrate and evaluate the model‐based approach in two case studies. In the first, we use the general recognition theory decision‐bound model of categorization (Ashby & Townsend, ) to infer each person's decision boundary for two categories of perceptual stimuli, and we use these inferences to make aggregated predictions about new stimuli. In the second, we use the generalized context model exemplar model of categorization (Nosofsky, ) to infer each person's selective attention for face stimuli, and we use these inferences to make aggregated predictions about withheld stimuli. In both case studies, we show that our method successfully predicts the category of unobserved stimuli, and we emphasize that the aggregated crowd decisions arise from psychologically interpretable processes and parameters. We conclude by discussing extensions and potential real‐world applications of the approach. (shrink)

We apply a cognitive modeling approach to the problem of measuring expertise on rank ordering problems. In these problems, people must order a set of items in terms of a given criterion (e.g., ordering American holidays through the calendar year). Using a cognitive model of behavior on this problem that allows for individual differences in knowledge, we are able to infer people's expertise directly from the rankings they provide. We show that our model-based measure of expertise outperforms self-report measures, taken (...) both before and after completing the ordering of items, in terms of correlation with the actual accuracy of the answers. These results apply to six general knowledge tasks, like ordering American holidays, and two prediction tasks, involving sporting and television competitions. Based on these results, we discuss the potential and limitations of using cognitive models in assessing expertise. (shrink)

While Tenenbaum and Griffiths impressively consolidate and extend Shepard's research in the areas of stimulus representation and generalization, there is a need for complexity measures to be developed to control the flexibility of their “hypothesis space” approach to representation. It may also be possible to extend their concept learning model to consider the fundamental issue of representational adaptation. [Tenenbaum & Griffiths].

Jones & Love (J&L) should have given more attention to Agnostic uses of Bayesian methods for the statistical analysis of models and data. Reliance on the frequentist analysis of Bayesian models has retarded their development and prevented their full evaluation. The Ecumenical integration of Bayesian statistics to analyze Bayesian models offers a better way to test their inferential and predictive capabilities.

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. (shrink)

In most decision-making situations, there is a plethora of information potentially available to people. Deciding what information to gather and what to ignore is no small feat. How do decision makers determine in what sequence to collect information and when to stop? In two experiments, we administered a version of the German cities task developed by Gigerenzer and Goldstein (1996), in which participants had to decide which of two cities had the larger population. Decision makers were not provided with the (...) names of the cities, but they were able to collect different kinds of cues for both response alternatives (e.g., “Does this city have a university?”) before making a decision. Our experiments differed in whether participants were free to determine the number of cues they examined. We demonstrate that a novel model, using hierarchical latent mixtures and Bayesian inference (Lee & Newell, 2011) provides a more complete description of the data from both experiments than simple conventional strategies, such as the take–the–best or the Weighted Additive heuristics. (shrink)

Glenberg's account falls short in several respects. Besides requiring clearer explication of basic concepts, his account fails to recognize the autonomous nature of perception. His account of what is remembered, and its description, is too static. His strictures against connectionist modeling might be overcome by combining the notions of psychological space and principled learning in an embodied and situated network.