Uncovering mental representations with Markov chain Monte Carlo

A key challenge for cognitive psychology is the investigation of mental representations, such as object categories, subjective probabilities, choice utilities, and memory traces. In many cases, these representations can be expressed as a non-negative function defined over a set of objects. We present a behavioral method for estimating these functions. Our approach uses people as components of a Markov chain Monte Carlo (MCMC) algorithm, a sophisticated sampling method originally developed in statistical physics. Experiments 1 and 2 verified the MCMC method by training participants on various category structures and then recovering those structures. Experiment 3 demonstrated that the MCMC method can be used estimate the structures of the real-world animal shape categories of giraffes, horses, dogs, and cats. Experiment 4 combined the MCMC method with multidimensional scaling to demonstrate how different accounts of the structure of categories, such as prototype and exemplar models, can be tested, producing samples from the categories of apples, oranges, and grapes.     

Modeling memory and perception

I present a framework for modeling memory, retrieval, perception, and their interactions. Recent versions of the models were inspired by Bayesian induction: We chose models that make optimal decisions conditioned on a memory/perceptual system with inherently noisy storage and retrieval. The resultant models are, fortunately, largely consistent with my models dating back to the 1960s, and are therefore natural successors. My recent articles have presented simplified models in order to focus on particular applications. This article takes a larger perspective and places the individual models in a more global framework. I will discuss (1) the storage of episodic traces, the accumulation of these into knowledge (e.g., lexical/semantic traces in the case of words), and the changes in knowledge caused by learning; (2) the retrieval of information from episodic memory and from general knowledge; (3) decisions concerning storage, retrieval, and responding. Examples of applications include episodic recognition and cued and free recall, perceptual identification (naming, yes–no and forced‐choice), lexical decision, and long‐term and short‐term priming.     

Extending Statistics of Extremes to Distributions Varying in Position and Scale and the Implications for Race Models

Race models are characterized by the largest or smallest of samples from n distributions. The asymptotic theory of extremes has demonstrated that for identically distributed, independent, and lower-bounded random variables, whose left tail approximates a power function, the distribution of the minimum tends toward a Weibull distribution as n increases. In this article, we remove the restriction of identically distributed random variables by letting the lower bound or the scale of the random variables be random variables themselves. We prove that the Weibull distribution is still the asymptotic distribution of the minimum and relate its parameters to the parameters of the input distributions. We discuss the potential use of such findings in models of psychological processes.     

Feature frequency effects in recognition memory

Rare words are usually better recognized than common words, a finding in recognition memory known as the word-frequency effect. Some theories predict the word-frequency effect because they assume that rare words consist of more distinctive features than do common words (e.g., Shiffrin & Steyvers's, 1997, REM theory). In this study, recognition memory was tested for words that vary in the commonness of their orthographic features, and we found that recognition was best for words made up of primarily rare letters. In addition, a mirror effect was observed: Words with rare letters had a higher hit rate and a lower false-alarm rate than did words with common letters. We also found that normative word frequency affects recognition independently of letter frequency. Therefore, the distinctiveness of a word's orthographic features is one, but not the only, factor necessary to explain the word-frequency effect.     

Confusion and compensation in visual perception: effects of spatiotemporal proximity and selective attention

The authors investigated spatial, temporal, and attentional manipulations in a short-term repetition priming paradigm. Brief primes produced a strong preference to choose the primed alternative, whereas long primes had the opposite effect. However, a 2nd brief presentation of a long prime produced a preference for the primed word despite the long total prime duration. These surprising results are explained by a computational model that posits the offsetting components of source confusion (prime features are confused with target features) and discounting (evidence from primed features is discounted). The authors obtained compelling evidence for these components by showing how they can cooperate or compete through different manipulations of prime salience. The model allows for dissociations between prime salience and the magnitude of priming, thereby providing a unified account of "subliminal" and "supraliminal" priming.     

An ARC-REM model for accuracy and response time in recognition and recall

This article presents a model for accuracy and response time (RT) in recognition and cued recall, fitted to free-response and signal-to-respond data from Experiment 1 of P. A. Nobel and R. M. Shiffrin (2001). The model posits that recognition operates through parallel activation in a single retrieval step and cued recall operates as a sequential search. Because the data for recognition showed that variations in list length and study time per list had a large effect on accuracy but a small or negligible effect on (a) free-response RT distributions and (b) retrieval dynamics in signal-to-respond, the timing of the recognition decision is based on an assessment of retrieval completion (ARC), rather than on a sufficiency of evidence in favor of 1 of the response options. By assuming within-trial forgetting, the model predicts both the dissociation of accuracy and RT and the finding that errors are slower than correct responses. For cued recall, this model was incorporated as the 1st step in a search consisting of cycles of sampling and recovery.     

Recognition of multiple-item probes

In the present study, we contrasted models in whichfamiliarity orstrength is the sole basis for recognition judgments (e.g., Gillund & Shiffrin, 1984) with models incorporating retrieval of specific information in a recall-like process (e.g., Humphreys, 1976, 1978; Humphreys & Bain, 1984). We also examined the possibility that an item’s “strength” is determined in part by the match between the verbal encoding contexts at study and at test. In two experiments, study items were presented in triplets. In Experiment 1 recognition was tested with all possible combinations of one-, two-, or three-item targets and distractors; in addition, three different decision criteria were employed in different lists. Experiment 2 included cued recognition among other test conditions. Recognition performance did not increase as more cues were added to the probe, a finding that is inconsistent with Humphreys’s model and other models of that type. Both studies were well fit by a version of the Search of Associative Memory model for recognition (Gillund & Shiffrin, 1984).     

The art of model development and testing

Mathematical and computer simulation modeling are often computationally demanding procedures, so much so that even certain parts of these procedures, such as parameter estimation, exceed the capacities and speed of the best modern computer facilities. A good deal of effort has therefore been dedicated to speeding up and making more efficient programs such as those that are meant to find a global minimum of a parameter space. Our experience, however, is that such well-explored technical procedures in fact represent some of the shortest components of the total set of procedures by which models are developed. In this article we discuss what elements take up the lion’s share of development time and speculate on what lessons can be drawn concerning the role of high-performance computing in such enterprises.