Traditional statistical model evaluation typically relies on goodness-of-fit testing and quantifying model complexity by counting parameters. Both of these practices may result in overfitting and have thereby contributed to the generalizability crisis. The information-theoretic principle of minimum description length addresses both of these concerns by filtering noise from the observed data and consequently increasing generalizability to unseen data.

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use of optimality assumptions. Through (...) these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

Model validation in computational cognitive psychology often relies on methods drawn from the testing of theories in experimental physics. However, applications of these methods to computational models in typical cognitive experiments can hide multiple, plausible sources of variation arising from human participants and from stochastic cognitive theories, encouraging a “model fixed, data variable” paradigm that makes it difficult to interpret model predictions and to account for individual differences. This article proposes a likelihood‐based, “data fixed, model variable” paradigm in which models (...) are treated as stochastic processes in experiments with participant‐to‐participant variation that can be applied to a broad range of mechanistic cognitive architectures. This article discusses the implementation and implications of this view in model validation, with a concrete focus on a simple class of ACT‐R models of cognition. This article is not intended as a recipe for broad application of these preliminary, proof‐of‐concept methods, but as a framework for communication between statisticians searching for interesting problems in the cognitive modeling sphere, and cognitive modelers interested in generalizing from deterministic to stochastic model validation, in the face of random variation in human experimental data. (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)

Models of intertemporal choice draw on three evaluation rules, which we compare in the restricted domain of choices between smaller sooner and larger later monetary outcomes. The hyperbolic discounting model proposes an alternative-based rule, in which options are evaluated separately. The interval discounting model proposes a hybrid rule, in which the outcomes are evaluated separately, but the delays to those outcomes are evaluated in comparison with one another. The tradeoff model proposes an attribute-based rule, in which both outcomes and delays (...) are evaluated in comparison with one another: People consider both the intervals between the outcomes and the compensations received or paid over those intervals. We compare highly general parametric functional forms of these models by means of a Bayesian analysis, a method of analysis not previously used in intertemporal choice. We find that the hyperbolic discounting model is outperformed by the interval discounting model, which, in turn, is outperformed by the tradeoff model. Our cognitive modeling is among the first to offer quantitative evidence against the conventional view that people make intertemporal choices by discounting the value of future outcomes, and in favor of the view that they directly compare options along the time and outcome attributes. (shrink)

The production of complex sequences like music or speech requires the rapid and temporally precise production of events (e.g., notes and chords), often at fast rates. Memory retrieval in these circumstances may rely on the simultaneous activation of both the current event and the surrounding context (Lashley, 1951). We describe an extension to a model of incremental retrieval in sequence production (Palmer & Pfordresher, 2003) that incorporates this logic to predict overall error rates and speed—accuracy trade-offs, as well as types (...) of serial ordering errors. The model—assumes that retrieval of the current event is influenced by activations of surrounding events. Activations of surrounding events increase over time, such that both the accessibility of distant events and overall accuracy increases at slower production rates. The model's predictions were tested in an experiment in which pianists performed unfamiliar music at 8 different tempi. Model fits to speed—accuracy data and to serial ordering errors support model predictions. Parameter fits to individual data further suggest that working memory contributes to the retrieval of serial order and overall accuracy is influenced in addition by motor dexterity and domain-specific skill. (shrink)

Severity of Test (SoT) is an alternative to Popper's logical falsification that solves a number of problems of the logical view. It was presented by Popper himself in 1963. SoT is a less sophisticated probabilistic model of hypothesis testing than Oaksford & Chater's (O&C's) information gain model, but it has a number of striking similarities. Moreover, it captures the intuition of everyday hypothesis testing.

A primary criterion on which models of cognition are evaluated is their ability to fit empirical data. To understand the reason why a model yields a good or poor fit, it is necessary to determine the data‐fitting potential (i.e., flexibility) of the model. In the first part of this article, methods for comparing models and studying their flexibility are reviewed, with a focus on parameter space partitioning (PSP), a general‐purpose method for analyzing and comparing all classes of cognitive models. PSP (...) is then demonstrated in the second part of the article in which two connectionist models of speech perception (TRACE and ARTphone) are compared to learn how design differences affect model flexibility. (shrink)

The production of complex sequences like music or speech requires the rapid and temporally precise production of events (e.g., notes and chords), often at fast rates. Memory retrieval in these circumstances may rely on the simultaneous activation of both the current event and the surrounding context (Lashley, 1951). We describe an extension to a model of incremental retrieval in sequence production (Palmer & Pfordresher, 2003) that incorporates this logic to predict overall error rates and speed—accuracy trade-offs, as well as types (...) of serial ordering errors. The model—assumes that retrieval of the current event is influenced by activations of surrounding events. Activations of surrounding events increase over time, such that both the accessibility of distant events and overall accuracy increases at slower production rates. The model's predictions were tested in an experiment in which pianists performed unfamiliar music at 8 different tempi. Model fits to speed—accuracy data and to serial ordering errors support model predictions. Parameter fits to individual data further suggest that working memory contributes to the retrieval of serial order and overall accuracy is influenced in addition by motor dexterity and domain-specific skill. (shrink)

Human cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. In Bayesian Rationality we argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some suggest that there is (...) a residual role for logic in understanding reasoning; and others put forward alternative formalisms for uncertain reasoning, or raise specific technical, methodological, or empirical challenges. In responding to these points, we aim to clarify the scope and limits of probability and logic in cognitive science; explore the meaning of the explanation of cognition; and re-evaluate the empirical case for Bayesian rationality. (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)

Computational modeling of the brain holds great promise as a bridge from brain to behavior. To fulfill this promise, however, it is not enough for models to be 'biologically plausible': models must be structurally accurate. Here, we analyze what this entails for so-called psychobiological models, models that address behavior as well as brain function in some detail. Structural accuracy may be supported by (1) a model's a priori plausibility, which comes from a reliance on evidence-based assumptions, (2) fitting existing data, (...) and (3) the derivation of new predictions. All three sources of support require modelers to be explicit about the ontology of the model, and require the existence of data constraining the modeling. For situations in which such data are only sparsely available, we suggest a new approach. If several models are constructed that together form a hierarchy of models, higher-level models can be constrained by lower-level models, and low-level models can be constrained by behavioral features of the higher-level models. Modeling the same substrate at different levels of representation, as proposed here, thus has benefits that exceed the merits of each model in the hierarchy on its own. (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)

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)

Cognitive modeling is the effort to understand the mind by implementing theories of the mind in computer code, producing measures comparable to human behavior and mental activity. The community of cognitive modelers has traditionally met twice every 3 years at the International Conference on Cognitive Modeling. In this special issue of topiCS, we present the best papers from the ICCM meeting. These best papers represent advances in the state of the art in cognitive modeling. Since ICCM was for the first (...) time also held jointly with the Society for Mathematical Psychology, we use this preface to also reflect on the similarities and differences between mathematical psychology and cognitive modeling. (shrink)

In this issue of topiCS, we present the best papers from the ICCM meeting. These best papers represent advances in the state of the art in cognitive modeling. Since ICCM was for the first time also held jointly with the Society for Mathematical Psychology, we use this preface to also reflect on the similarities and differences between mathematical psychology and cognitive modeling.

Decisions in the environmental and in particular the climate domain are burdened with uncertainty. Here, we focus on uncertainties faced by individuals when making decisions about environmental behavior, and we use the statistical sampling framework to develop a classification of different sources of uncertainty they encounter. We then map these sources to different public policy strategies aiming to help individuals cope with uncertainty when making environmental decisions.

Ormerod and Chronicle reported that optimal solutions to traveling salesperson problems were judged to be aesthetically more pleasing than poorer solutions and that solutions with more convex hull nodes were rated as better figures. To test these conclusions, solution regularity and the number of potential intersections were held constant, whereas solution optimality, the number of internal nodes, and the number of nearest neighbors in each solution were varied factorially. The results did not support the view that the convex hull is (...) an important determinant of figural attractiveness. Also, in contrast to the findings of Ormerod and Chronicle, there were consistent individual differences. Participants appeared to be divided as to whether the most attractive figure enclosed a given area within a perimeter of minimum or maximum length. It is concluded that future research in this area cannot afford to focus exclusively on group performance measures. (shrink)