Fig. 5.

Qualitative replication of, as well as predictions related to, the results reported by Wolpe et al.²². a Qualitative replication of the experimental results (left panel) by our Bayesian model (right panel). b The action-outcome binding increases under heightened uncertainty. However, causality is less detected when the causal prior is lower, which decreases the action-outcome binding effect. The best estimates of the Bayesian model in a were obtained from different causal prior strengths, specifically P(ξ = 1) is 0.9, 0.6, and 0.5 (marked by the colored dots) for the low, intermediate, and high tone uncertainty conditions, respectively. c, d The causal prior strengths that correspond to each condition were used for the Bayesian estimate of the action-outcome timing interval ${\widehat{t}}_{\mathrm{O}}-{\widehat{t}}_{\mathrm{A}}$ in the baseline and operant conditions. The Bayesian estimate follows the sensory inputs in the baseline condition where all trials are acausal, but shifts towards the prior assumption, τ_O − τ_A ≈ μ_AO, when causality is detected. The temporal window of τ_O − τ_A for detecting causality is wider when the outcome uncertainty is lower, which means more instances demonstrate binding