Figure 1. Audiovisual localization paradigm and Bayesian causal inference model for learning visual reliability.

(A) Visual (V) signals (cloud of 20 bright dots) were presented every 200 ms for 32 ms. The cloud’s location mean was temporally independently resampled from five possible locations (−10°, −5°, 0°, 5°, 10°) with an inter-trial asynchrony jittered between 1.4 and 2.8 s. In synchrony with the change in the cloud’s mean location, the dots changed their color and a sound was presented (AV signal) which the participants localized using five response buttons. The location of the sound was sampled from the two possible locations adjacent to the visual cloud’s mean location (i.e. ±5° AV spatial). (B) The generative model for the Bayesian learner explicitly modeled the potential causal structures, that is whether visual (V_i) signals and an auditory (A) signal were generated by one common audiovisual source S_t, that is C = 1, or by two independent sources S_Vt and S_At, that is C = 2 (n.b. only the model component for the common source case is shown to illustrate the temporal updating, for complete generative model, see Figure 1—figure supplement 1). Importantly, the reliability (i.e. 1/variance) of the visual signal at time t (λ_t) depends on the reliability of the previous visual signal (λ_t-1) for both model components (i.e. common and independent sources).

Figure 1—figure supplement 1. Generative model for the Bayesian learner.

The Bayesian Causal Inference model explicitly models whether auditory and visual signals are generated by one common (C = 1) or two independent sources (C = 2) (for further details see Körding et al., 2007). We extend this Bayesian Causal Inference model into a Bayesian learning model by making the visual reliability (${\lambda }_{V,t}$, i.e. the inverse of uncertainty or variance) of the current trial dependent on the previous trial.