Mathematical Models of Cognitive Control: Design, Comparison, and Optimization

Abstract

In this thesis, we investigate human decision making dynamics in a series of simple perceptual decision making tasks. The level of caution with which a human subject responds to stimuli is of central interest, since it influences the speed and accuracy of responses. We study the role of caution parameters in models of cognitive control processes.

We first investigate the influence of stimulus likelihood on human error dynamics in sequential two-alternative choice tasks. Errors are understood to increase in frequency when caution is low. When subjects repeatedly discriminate between two stimuli, their error rates and mean reaction times (RTs) systematically depend on prior sequences of stimuli. We analyze sequential effects on RTs, showing that relationships among prior stimulus sequences and the corresponding RTs for correct trials, error trials, and averaged over all trials are significantly influenced by the probability of alternations. Finally, we show that simple, sequential updates to the initial condition and thresholds of a pure drift diffusion model (DDM) can account for the trends in RT for correct and error trials. Our results suggest that error-based parameter adjustments are critical to modeling sequential effects. These relationships have not been captured by previous models.

In the remainder of the thesis, we compare models of human choice dynamics in tasks in which subjects must trade off between speed and accuracy in order to maximize reward rates. Caution is of critical importance: while errors decrease in frequency as caution increases, decision time increases. Direct manipulation of caution provides a framework with which to compare models. Recent work has compared the predictions of the Linear Ballistic Accumulator (LBA) and the DDM for simple RT tasks but has identified no important qualitative differences between the predictions of the two models. Comparing the fits of the two models for simple RT tasks in which subjects attempt to maximize reward rate, we show that while the pure DDM predicts a single optimal performance curve, the curve for the LBA varies significantly with model parameters. Critically, we find that while reward seeking behavior is predicted on average by an increase in caution in the DDMs, the same behavior in the best-fitting LBA model is instead predicted by a decrease in caution.