Figure 1. Two alternative forced choice (2AFC) tasks in dynamic environments.
(A) Possible timescales of environmental dynamics: 1) The state (S+ or S−), or the quality of the evidence (e.g., coherence of random dot motion stimulus) may switch within a trial5, 6, 10, or 2) across trials11–13; 3) The hazard rate (switching rate, h), can change across blocks of trials6, 9. (B) In a dynamic 2AFC task, a two-state Markov chain with hazard rate h determines the state. (Bi) The current state (correct hypothesis) is either S+ (red) or S− (yellow). (Bii) Conditional densities of the observations, f±(ξ) = P(ξ|S±), shown as Gaussians with means ±μ and standard deviation σ. (C) Evidence discounting is shaped by the environmental timescale: (Top) In slow environments, posterior probabilities over the states, P(S±|ξ1:4); are more strongly influenced by the cumulative effect of past observations, ξ1:3, (darker shades of the observations, ξi, indicate higher weight) and thus points to S+. (Bottom) If changes are fast, beliefs depend more strongly on the current observation, ξ4, which outweighs older evidence and points to S−.