Categorical estimation task: Transient performance after changes. (A) At each time step, the agent sees one out of five possible categories (black dots) drawn from a categorical distribution with parameters $pt$⁠. Occasional abrupt changes happen with probability $pc$ and are marked with red lines. After each change, a new $pt$ vector is drawn from a Dirichlet distribution with stochasticity parameter $s$⁠. In this example, $s=1$ and $pc=0.01$⁠. (B) Mean squared error for the estimation of $pt$ at each time step $n$ after an environmental change, that is, the average of $MSE[Θ^t|Rt=n]$ over time; $s=0.14,pc=0.01$ (left panel) and $s=5,pc=0.005$ (right panel). The shaded area corresponds to the standard error of the mean. Abbreviations: pf$N$⁠: Particle Filtering with $N$ particles; MP$N$⁠: Message Passing with $N$ particles; VarSMiLe: Variational SMiLe; SOR$N$⁠: Stratisfied Optimal Resampling with $N$ particles (Fearnhead & Liu, 2007); SMiLe: Faraji et al. (2018); Leaky: Leaky Integrator; Exact Bayes: Adams and MacKay (2007).