Augmenting the Bayesian Ornstein-Uhlenbeck model for retest learning: simulation study

Measuring cognitive performance is traditionally done using single-shot measurement protocols, relying on standardized tests which say little about how cognition fluctuates through days and different contexts. Many tools and experimental protocols have thus been developed to address these issues: the central idea is to administer either ultra-brief versions of traditional tests or validated “cognitive games” multiple times per day over multiple days, across multiple measurement bursts. By using such tools, we can obtain time-dependent paths of subjects as their cognitive performance “ebbs and flows” through the day. What then remains is to model this new kind of data; while many approaches have used a discrete time framework, more recently continuous-time models have attracted growing interest. Here, we present an extension of the Ornstein-Uhlenbeck (OU) model, which has been previously used, within affective science, to describe emotional regulation dynamics, by augmenting it with a Double Exponential (DE) model. The DE formulation has been used in cognitive science to describe learning mechanisms across bursts. Therefore, we sought to combine them to describe a stochastic process which moves towards an asymptotic level within a burst, fluctuating about an evolving mean, with changes in asymptotic performance and forgetting mechanisms between bursts. Using simulated data informed by the MindTrack study, we present preliminary results on the within-burst half of the model, implemented via two Bayesian frameworks – PyMC and Stan – while investigating parameter identification and recovery, limited to a single-burst design.