The question of how one should decide among competing explanations of data is at the heart of the scientific enterprise. Computational models of cognition are increasingly being advanced as explanations of behavior. The success of this line of inquiry depends on the development of robust methods to guide the evaluation and selection of these models. This article introduces a method of selecting among mathematical models of cognition known as minimum description length, which provides an intuitive and theoretically well-grounded understanding of why one model should be chosen. A central but elusive concept in model selection, complexity, can also be derived with the method. The adequacy of the method is demonstrated in 3 areas of cognitive modeling: psychophysics, information integration, and categorization. How should one choose among competing theoretical explanations of data? This question is at the heart of the scientific enterprise, regardless of whether verbal models are being tested in an experimental setting or computational models are being evaluated in simulations. A number of criteria have been proposed to assist in this endeavor, summarized nicely by Jacobs and Grainger

predictions of exemplar models and that supported prototype models. In the authors ’ view, this evidence confounded the issue of the nature of the category representation with the type of response rule (probabilistic vs. deterministic) that was used. Also, their designs did not test whether the prototype models correctly predicted generalization performance. The present work demonstrates that an exemplar model that includes a response-scaling mechanism provides a natural account of all of Smith et al.’s experimental results. Furthermore, the exemplar model predicts classification performance better than the prototype models when novel transfer stimuli are included in the experimental designs. A classic issue in cognitive psychology concerns the manner in which people represent categories in memory. According to prototype models (Homa, 1984; Posner & Keele, 1968; Reed, 1972), people represent categories by forming a summary representation that is a central tendency of all of the experienced members of a

(2-AFC) perceptual identification in a short-term priming task. For repetition priming, passive viewing of primes resulted in a preference to choose repeated words, but actively responding to primes resulted in a preference against choosing repeated words. These results were explained with a computational model, responding optimally with unknown sources of evidence (ROUSE), using the offsetting mechanisms of source confusion and discounting. An analysis of ROUSE revealed conditions under which discounting efficacy should diminish, causing a preference for primed words even with active prime processing. Two new studies confirm 2 such conditions: very short target flash durations and very low similarity between primes and primed choice words. These a priori predictions contrast with the a posteriori data fits of a multinomial model developed by R. Ratcliff and G. McKoon (2001). Recent use of forced-choice testing in perceptual-identification priming tasks suggests that priming (both short- and long-term) is due more to decisional biases than to enhanced perceptual processing

For over 200 years, philosophers and mathematicians have been using probability theory to describe human cognition. While the theory of probabilities was first developed as a means of analyzing games of chance, it quickly took on a larger and deeper significance as a formal account of how rational agents should reason in situations of uncertainty

... framework of cognitive psychology in favor of the framework of nonlinear dynamical systems theory. Van Orden et al. presented evidence that“purposive behavior originates in self-organized criticality ” (p. 333). Here, the authors show that Van Orden et al.’s analyses do not test their hypotheses. Further, the authors argue that a confirmation of Van Orden et al.’s hypotheses would not have constituted firm evidence in support of their framework. Finally, the absence of a specific model for how self-organized criticality produces the observed behavior makes it very difficult to derive testable predictions. The authors conclude that the proposed paradigm shift is presently unwarranted.

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Provenance of correlations in psychological data There are few truisms in the field of psychology, but one of them is surely that measurement error is found in all experiments. Data are inevitably produced that do not perfectly reflect the logic imposed by the experimental design. To the extent that a psychological experiment succeeds in measuring something or in making some sort of distinction, the data will partially reflect the design, and this leads to a way of thinking about data that is found throughout all the experimental sciences: data � signal � noise. This innocent equation almost always contains an implicit but critical assumption: that the noise may be regarded as independent samples from some distribution— typically taken to be the Gaussian distribution. In this way, the residual error is conceived of as a featureless background of white noise in which the interesting part, the treatment means, are more or less buried. Often this conception of data is justified. Whenever there is random assignment to cells and each participant contributes a single datum, errors may be expected to be uncorrelated. However, in all of sensory psychophysics and most of cognitive psychology, single individuals respond to entire blocks of trials in a given experimental session. Here, the residual error will develop correlations by virtue of the circumstance that the response history was laid down by a nervous system that has memory. In many situations, these correlations are little more than a Preparation of this article was supported by NIMH Grants R01-

Throughout this book, the topic of order-restricted inference is dealt with almost exclusively from a Bayesian perspective. Some readers may wonder why the other main school for statistical inference – frequentist inference – has received so little attention here. Isn’t it true that in the field of psychology, almost all inference is frequentist inference? The first goal of this chapter is to highlight why frequentist inference is a less-thanideal method for statistical inference. The most fundamental limitation of standard frequentist inference is that it does not condition on the observed data. The resulting paradoxes have sparked a philosophical debate that statistical practitioners have conveniently ignored. What cannot be so easily ignored are the practical limitations of frequentist inference, such as its restriction to nested model comparisons. The second goal of this chapter is to highlight the theoretical and practical advantages of a Bayesian analysis. From a theoretical perspective, Bayesian inference is principled and prescriptive, and – in contrast to frequentist inference – a method that does condition on the observed data. From a practical perspective, Bayesian inference

We present a new model for lexical decision, REM-LD, that is based on REM theory (e.g., Shiffrin & Steyvers, 1997). REM-LD uses a principled (i.e., Bayes ’ rule) decision process that simultaneously considers the diagnosticity of the evidence for the ‘WORD ’ response and the ‘NONWORD ’ response. The model calculates the odds ratio that the presented stimulus is a word or a nonword by accumulating likelihood ratios for each lexical entry in a small neighborhood of similar words. We report two experiments that used the signal-to-respond paradigm to obtain information about the time course of lexical processing. Experiment 1 verified the prediction of the model that the frequency of the word stimuli affects performance for nonword stimuli. Experiment 2 was done to study the effects of nonword lexicality, word frequency, and repetition priming and to demonstrate how REM-LD can account for the observed results. We discuss how REM-LD can be extended to account for effects of phonology such as the pseudohomophone effect, and how REM-LD can predict response times in the popular ‘respond-when-ready ’ paradigm. Several other quantitative models of lexical decision are evaluated with respect to the findings reported here.