Approximating Bayesian Inference through Model Simulation.

The ultimate test of the validity of a cognitive theory is its ability to predict patterns of empirical data. Cognitive models formalize this test by making specific processing assumptions that yield mathematical predictions, and the mathematics allow the models to be fitted to data. As the field of cognitive science has grown to address increasingly complex problems, so too has the complexity of models increased. Some models have become so complex that the mathematics detailing their predictions are intractable, meaning that the model can only be simulated. Recently, new Bayesian techniques have made it possible to fit these simulation-based models to data. These techniques have even allowed simulation-based models to transition into neuroscience, where tests of cognitive theories can be biologically substantiated.

The neural basis of value accumulation in intertemporal choice.

Making intertemporal choices (choosing between rewards available at different points in time) requires determining and comparing the subjective values of available rewards. Several studies have found converging evidence identifying the neural systems that encode subjective value in intertemporal choice. However, the neural mechanisms responsible for the process that produces intertemporal decisions on the basis of subjective values have not been investigated. Using model-based and connectivity analyses of functional magnetic resonance imaging data, we investigated the neural mechanisms underlying the value-accumulation process by which subjective value guides intertemporal decisions. Our results show that the dorsomedial frontal cortex, bilateral posterior parietal cortex, and bilateral lateral prefrontal cortex are all involved in the accumulation of subjective value for the purpose of action selection. Our findings establish a mechanistic framework for understanding frontoparietal contributions to intertemporal choice and suggest that value-accumulation processes in the frontoparietal cortex may be a general mechanism for value-based choice.

On the ability to inhibit thought and action: general and special theories of an act of control.

Response inhibition is an important act of control in many domains of psychology and neuroscience. It is often studied in a stop-signal task that requires subjects to inhibit an ongoing action in response to a stop signal. Performance in the stop-signal task is understood as a race between a go process that underlies the action and a stop process that inhibits the action. Responses are inhibited if the stop process finishes before the go process. The finishing time of the stop process is not directly observable; a mathematical model is required to estimate its duration. Logan and Cowan (1984) developed an independent race model that is widely used for this purpose. We present a general race model that extends the independent race model to account for the role of choice in go and stop processes, and a special race model that assumes each runner is a stochastic accumulator governed by a diffusion process. We apply the models to 2 data sets to test assumptions about selective influence of capacity limitations on drift rates and strategies on thresholds, which are largely confirmed. The model provides estimates of distributions of stop-signal response times, which previous models could not estimate. We discuss implications of viewing cognitive control as the result of a repertoire of acts of control tailored to different tasks and situations.

Hierarchical approximate Bayesian computation.

Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model's parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper, we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function.

Likelihood-free Bayesian analysis of memory models.

Many influential memory models are computational in the sense that their predictions are derived through simulation. This means that it is difficult or impossible to write down a probability distribution or likelihood that characterizes the random behavior of the data as a function of the model's parameters. In turn, the lack of a likelihood means that these models cannot be directly fitted to data using traditional techniques. In particular, standard Bayesian analyses of such models are impossible. In this article, we examine how a new procedure called approximate Bayesian computation (ABC), a method for Bayesian analysis that circumvents the evaluation of the likelihood, can be used to fit computational models to memory data. In particular, we investigate the bind cue decide model of episodic memory (Dennis & Humphreys, 2001) and the retrieving effectively from memory model (Shiffrin & Steyvers, 1997). We fit hierarchical versions of each model to the data of Dennis, Lee, and Kinnell (2008) and Kinnell and Dennis (2012). The ABC analysis permits us to explore the relationships between the parameters in each model as well as evaluate their relative fits to data-analyses that were not previously possible.

A dynamic stimulus-driven model of signal detection.

Signal detection theory forms the core of many current models of cognition, including memory, choice, and categorization. However, the classic signal detection model presumes the a priori existence of fixed stimulus representations--usually Gaussian distributions--even when the observer has no experience with the task. Furthermore, the classic signal detection model requires the observer to place a response criterion along the axis of stimulus strength, and without theoretical elaboration, this criterion is fixed and independent of the observer's experience. We present a dynamic, adaptive model that addresses these 2 long-standing issues. Our model describes how the stimulus representation can develop from a rough subjective prior and thereby explains changes in signal detection performance over time. The model structure also provides a basis for the signal detection decision that does not require the placement of a criterion along the axis of stimulus strength. We present simulations of the model to examine its behavior and several experiments that provide data to test the model. We also fit the model to recognition memory data and discuss the role that feedback plays in establishing stimulus representations.

An application of the poisson race model to confidence calibration.

In tasks as diverse as stock market predictions and jury deliberations, a person's feelings of confidence in the appropriateness of different choices often impact that person's final choice. The current study examines the mathematical modeling of confidence calibration in a simple dual-choice task. Experiments are motivated by an accumulator model, which proposes that information supporting each alternative accrues on separate counters. The observer responds in favor of whichever alternative's counter first hits a designated threshold. Confidence can then be scaled from the difference between the counters at the time that the observer makes a response. The authors examine the overconfidence result in general and present new findings dealing with the effect of response bias on confidence calibration.

Response reversals in recognition memory.

Using a dynamic sequential sampling model and a recently proposed model for confidence judgments in recognition memory (T. Van Zandt, 2000b), the authors examine the tendency for rememberers to reverse their responses after a primary decision. In 4 experiments, speeded "old"-"new" decisions were made under bias followed by a 2nd response', either a confidence judgment or another simple choice. The data from these experiments showed that participants know when they have made a mistake and that they respond to this knowledge by reversing their responses. Response reversals are thus shown to be important for constructing models of the response-selection process in recognition memory.