Time to jump: Exploring the distribution of noise in evidence accumulation as a function of time pressure

The diffusion model (DM; Ratcliff, 1978) assumes that decisions originate from a continuous evidence accumulation process that is subject to Gaussian noise. The Lévy flight model (LFM; Voss et al., 2019) provides a modification thereof. Specifically, the LFM assumes accumulation noise to follow a more heavy-tailed distribution which allows for sudden large changes in the amount of accumulated evidence (i.e., jumps in evidence accumulation). The heavy-tailedness of the noise distribution is governed by the additional free parameter α. A previous study found α to be lower and, thus, jumps in evidence accumulation to be more prevalent under speed instructions. Building upon this finding, we also compared speed versus accuracy conditions using a letter-number discrimination task. However, aiming to contribute to a deeper understanding of the behavior of α under different levels of time pressure, we further intensified time pressure by imposing a response deadline of 500 ms in one condition. Because the altered noise distribution renders the LFM’s likelihood intractable, we used the simulation-based deep learning framework BayesFlow for our analyses. We found that, for most participants in the accuracy condition, accumulation noise was (nearly) normally distributed. By contrast, for most participants under intensified time pressure, accumulation noise was best described by distributions with remarkably heavy tails. Accordingly, the prevalence of jumps in evidence accumulation increased with time pressure. Importantly, corresponding α-values were clearly lower than those reported in all previous studies. Comparisons of the fit of different variants of the DM and LFM alongside implications for modeling decision processes under (deadline-based) time pressure are discussed.