Fundamental tools for developing likelihood functions within ACT-R

Likelihood functions are an integral component of statistical approaches to parameter estimation and model evaluation. However, likelihood functions are rarely used in cognitive architectures due, in part, to challenges in their derivation, and the lack of accessible tutorials. In this tutorial, we present fundamental concepts and tools for developing analytic likelihood functions for the ACT-R cognitive architecture. These tools are based on statistical concepts such as serial vs. parallel process, convolution, minimum/maximum processing time, and mixtures. Importantly, these statistical concepts are highly composable, allowing them to be combined to form likelihood functions for many models. We demonstrate how to apply these tools within the context of Bayesian parameter estimation using five models taken from the standard ACT-R tutorial. Although the tutorial focuses on ACT-R due to its prevalence, the concepts covered within the tutorial are applicable to other cognitive architectures.