Partial derivatives and an adaptive rejection sampler for the Wiener diffusion model

The Wiener diffusion model (and its extensions in terms of trial-by-trial variability in drift rate, starting point, and non-decision time) is one of the most frequently used cognitive models for binary response tasks. A key advantage of this model framework is that it allows for jointly modeling response frequency and latency. In Hartmann and Klauer (2021) we derived the partial derivatives of th diffusion-model density with respect to up to seven model parameters as well as with respect to the response time itself. Moreover, we developed an R package (WienR) that can be used to calculate these partial derivatives (as well as the PDFs and CDFs) of the response time distribution conditional on one of the two possible responses. In Hartmann, Meyer-Grant, and Klauer (2022) we further extended the WienR package by developing and implementing an efficient adaptive rejection sampler (ARS) that builds on the above-mentioned partial derivatives. In the present talk, the partial derivatives, the ARS method, and the WienR package will be introduced.