Adam N. Sanborn

Rational Approximations to Rational Models: Alternative Algorithms for Category Learning

Rational models of cognition typically consider the abstract computational problems posed by the environment, assuming that people are capable of optimally solving those problems. This differs from more traditional formal models of cognition, which focus on the psychological processes responsible for behavior. A basic challenge for rational models is thus explaining how optimal solutions can be approximated by psychological processes. We outline a general strategy for answering this question, namely to explore the psychological plausibility of approximation algorithms developed in computer science and statistics. In particular, we argue that Monte Carlo methods provide a source of rational process models that connect optimal solutions to psychological processes. We support this argument through a detailed example, applying this approach to Andersons (1990, 1991) rational model of categorization (RMC), which involves a particularly challenging computational problem. Drawing on a connection between the RMC and ideas from nonparametric Bayesian statistics, we propose 2 alternative algorithms for approximate inference in this model. The algorithms we consider include Gibbs sampling, a procedure appropriate when all stimuli are presented simultaneously, and particle filters, which sequentially approximate the posterior distribution with a small number of samples that are updated as new data become available. Applying these algorithms to several existing datasets shows that a particle filter with a single particle provides a good description of human inferences.

Exemplar models as a mechanism for performing Bayesian inference

Probabilistic models have recently received much attention as accounts of human cognition. However, most research in which probabilistic models have been used has been focused on formulating the abstract problems behind cognitive tasks and their optimal solutions, rather than on mechanisms that could implement these solutions. Exemplar models are a successful class of psychological process models in which an inventory of stored examples is used to solve problems such as identification, categorization, and function learning. We show that exemplar models can be used to perform a sophisticated form of Monte Carlo approximation known as importance sampling and thus provide a way to perform approximate Bayesian inference. Simulations of Bayesian inference in speech perception, generalization along a single dimension, making predictions about everyday events, concept learning, and reconstruction from memory show that exemplar models can often account for human performance with only a few exemplars, for both simple and relatively complex prior distributions. These results suggest that exemplar models provide a possible mechanism for implementing at least some forms of Bayesian inference.

Reconciling intuitive physics and newtonian mechanics for colliding objects

People have strong intuitions about the influence objects exert upon one another when they collide. Because peoples judgments appear to deviate from Newtonian mechanics, psychologists have suggested that people depend on a variety of task-specific heuristics. This leaves open the question of how these heuristics could be chosen, and how to integrate them into a unified model that can explain human judgments across a wide range of physical reasoning tasks. We propose an alternative framework, in which peoples judgments are based on optimal statistical inference over a Newtonian physical model that incorporates sensory noise and intrinsic uncertainty about the physical properties of the objects being viewed. This noisy Newton framework can be applied to a multitude of judgments, with peoples answers determined by the uncertainty they have for physical variables and the constraints of Newtonian mechanics. We investigate a range of effects in mass judgments that have been taken as strong evidence for heuristic use and show that they are well explained by the interplay between Newtonian constraints and sensory uncertainty. We also consider an extended model that handles causality judgments, and obtain good quantitative agreement with human judgments across tasks that involve different judgment types with a single consistent set of parameters.

Model evaluation using grouped or individual data

Analyzing the data of individuals has several advantages over analyzing the data combined across the individuals (the latter we term group analysis): Grouping can distort the form of data, and different individuals might perform the task using different processes and parameters. These factors notwithstanding, we demonstrate conditions in which group analysis outperforms individual analysis. Such conditions include those in which there are relatively few trials per subject per condition, a situation that sometimes introduces distortions and biases when models are fit and parameters are estimated. We employed a simulation technique in which data were generated from each of two known models, each with parameter variation across simulated individuals. We examined how well the generating model and its competitor each fared in fitting (both sets of) the data, using both individual and group analysis. We examined the accuracy of model selection (the probability that the correct model would be selected by the analysis method). Trials per condition and individuals per experiment were varied systematically. Three pairs of cognitive models were compared: exponential versus power models of forgetting, generalized context versus prototype models of categorization, and the fuzzy logical model of perception versus the linear integration model of information integration. We show that there are situations in which small numbers of trials per condition cause group analysis to outperform individual analysis. Additional tables and figures may be downloaded from the Psychonomic Society Archive of Norms, Stimuli, and Data, www.psychonomic.org/archive.

Bridging Levels of Analysis for Probabilistic Models of Cognition

Probabilistic models of cognition characterize the abstract computational problems underlying inductive inferences and identify their ideal solutions. This approach differs from traditional methods of investigating human cognition, which focus on identifying the cognitive or neural processes that underlie behavior and therefore concern alternative levels of analysis. To evaluate the theoretical implications of probabilistic models and increase their predictive power, we must understand the relationships between theories at these different levels of analysis. One strategy for bridging levels of analysis is to explore cognitive processes that have a direct link to probabilistic inference. Recent research employing this strategy has focused on the possibility that the Monte Carlo principle—which concerns sampling from probability distributions in order to perform computations—provides a way to link probabilistic models of cognition to more concrete cognitive and neural processes.

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.

Environmental Support Promotes Expertise-Based Mitigation of Age Differences on Pilot Communication Tasks

The authors investigated whether expertise is more likely to mitigate age declines when experts rely on environmental support in a pilot/Air Traffic Control (ATC) communication task. Pilots and nonpilots listened to ATC messages that described a route through an airspace, while they referred to a chart of the airspace. They read back (repeated) each message and then answered a probe question about the route. In a preliminary study, participants could take notes while listening to the messages and performing the read-back and probe tasks. In Experiment 1, opportunity to take notes was manipulated. Note taking determined when expertise mitigated age differences on the read-back task. With note taking, read-back accuracy declined with age for nonpilots but not for pilots. Without note taking, similar age-related declines occurred for pilots and nonpilots. Benefits of expertise, younger age, and note taking occurred for probe accuracy, but mitigation did not occur. The findings suggest that older adults take advantage of a domain-relevant form of environmental support (note taking) to maintain performance on some complex tasks despite typical age-related declines in cognitive ability.

Bayesian Brains without Probabilities

Bayesian explanations have swept through cognitive science over the past two decades, from intuitive physics and causal learning, to perception, motor control and language. Yet people flounder with even the simplest probability questions. What explains this apparent paradox? How can a supposedly Bayesian brain reason so poorly with probabilities? In this paper, we propose a direct and perhaps unexpected answer: that Bayesian brains need not represent or calculate probabilities at all and are, indeed, poorly adapted to do so. Instead, the brain is a Bayesian sampler. Only with infinite samples does a Bayesian sampler conform to the laws of probability; with finite samples it systematically generates classic probabilistic reasoning errors, including the unpacking effect, base-rate neglect, and the conjunction fallacy.

Better quality sleep promotes daytime physical activity in patients with chronic pain? A multilevel analysis of the within-person relationship.

Background Promoting physical activity is key to the management of chronic pain, but little is understood about the factors facilitating an individual’s engagement in physical activity on a day-to-day basis. This study examined the within-person effect of sleep on next day physical activity in patients with chronic pain and insomnia. Methods 119 chronic pain patients monitored their sleep and physical activity for a week in their usual sleeping and living environment. Physical activity was measured using actigraphy to provide a mean activity score each hour. Sleep was estimated with actigraphy and an electronic diary, providing an objective and subjective index of sleep efficiency (A-SE, SE) and a sleep quality rating (SQ). The individual and relative roles of these sleep parameters, as well as morning ratings of pain and mood, in predicting subsequent physical activity were examined in multilevel models that took into account variations in relationships at the ‘Day’ and ‘Participant’ levels. Results Of the 5 plausible predictors SQ was the only significant within-person predictor of subsequent physical activity, such that nights of higher sleep quality were followed by days of more physical activity, from noon to 11pm. The temporal association was not explained by potential confounders such as morning pain, mood or effects of the circadian rhythm. Conclusions In the absence of interventions, chronic pain patients spontaneously engaged in more physical activity following a better night of sleep. Improving nighttime sleep may well be a novel avenue for promoting daytime physical activity in patients with chronic pain.

The frequentist implications of optional stopping on Bayesian hypothesis tests

Null hypothesis significance testing (NHST) is the most commonly used statistical methodology in psychology. The probability of achieving a value as extreme or more extreme than the statistic obtained from the data is evaluated, and if it is low enough, the null hypothesis is rejected. However, because common experimental practice often clashes with the assumptions underlying NHST, these calculated probabilities are often incorrect. Most commonly, experimenters use tests that assume that sample sizes are fixed in advance of data collection but then use the data to determine when to stop; in the limit, experimenters can use data monitoring to guarantee that the null hypothesis will be rejected. Bayesian hypothesis testing (BHT) provides a solution to these ills because the stopping rule used is irrelevant to the calculation of a Bayes factor. In addition, there are strong mathematical guarantees on the frequentist properties of BHT that are comforting for researchers concerned that stopping rules could influence the Bayes factors produced. Here, we show that these guaranteed bounds have limited scope and often do not apply in psychological research. Specifically, we quantitatively demonstrate the impact of optional stopping on the resulting Bayes factors in two common situations: (1) when the truth is a combination of the hypotheses, such as in a heterogeneous population, and (2) when a hypothesis is composite—taking multiple parameter values—such as the alternative hypothesis in a t-test. We found that, for these situations, while the Bayesian interpretation remains correct regardless of the stopping rule used, the choice of stopping rule can, in some situations, greatly increase the chance of experimenters finding evidence in the direction they desire. We suggest ways to control these frequentist implications of stopping rules on BHT.