“…A formal model comparison between the VD model and the hyperbolic extension using PSIS-LOO and WAIC shows that both models have a similar predictive performance. This work accords with other studies that propose humans are sensitive to higher-order variables that control the dynamics of the environment (Behrens et al, 2007;Courville, Daw, & Touretzky, 2006;McGuire, Nassar, Gold, & Kable, 2014;Meder et al, 2017;Ricci & Gallistel, 2017;Wittmann et al, 2016;Yu & Dayan, 2005). In particular, our model suggests that when the environment is changing smoothly at a variable velocity, subjects have an estimate of this quantity and use it to make predictions as suggested in figure 2.…”