A, Flow diagram of the decision process.

<p>Models differ along three dimensions: whether precision is equal or variable, the observer’s assumption about precision, and the observer’s integration rule. B, Examples of probability density functions over encoding precision for a high-reliability and a low-reliability stimulus (long and short ellipse, respectively) in the variable-precision model. Dashed lines indicate the means. C, The generative model shows statistical dependencies between variables. <i>C</i>: change occurrence (0 or 1); Δ: magnitude of change; <b>Δ</b>: vector of change magnitudes at all locations; <b>θ</b> and <b>φ</b>: vectors of stimulus orientations in the first and second displays, respectively; <b>x</b> and <b>y</b>: vectors of measurements of the stimulus orientations. The spatial, temporal, and structural complexities of the task can be recognized in the vector nature of the orientation variables, the two “branches”, and the number of layers, respectively.