Simulated effects of four computational imperfections.

(A) Schematic illustration of a single trial in the simulation that was aimed at assessing how computational imperfections affect the optimal observer’s decision variable. On each trial, a stimulus set s and stimulus observations x were drawn from the generative model for the visual search task with 10% external uncertainty. Next, x was provided as input to the Flawless Bayesian model and to a variant of this model with a computational imperfection (e.g., a wrong belief about experimental parameter σexternal). Both models produce a decision variable, d(x). We denote the difference between these two decision variables by Δd(x), which can be thought of as a computational error. A total of 1 million trials were simulated using four different types of computational imperfection: (1) Gaussian noise on the local decision variables; (2) an overestimated value of σexternal; (3) overestimated values of σlow and σhigh; (4) item-to-item and trial-to-trial noise on σlow and σhigh. (B) The distribution of Δd(x) under each simulated computational imperfection (gray areas). In all four cases, this distribution is reasonably well approximated by a Gaussian distribution (black curves). The percentages indicate the accuracy loss caused by the computational imperfection; parameters μ and σ indicate the mean and standard deviation of the Gaussian fitted to each distribution. (C) The distribution of Δd(x) in a model that contains all four tested imperfections simultaneously.