Figure 7. Example of how Signal Detection Theory is used to compute model responses across trials.

(A) Across trials, the posterior distributions of the audio and visual stimuli can be considered to directly compute the proportion of sound-first responses. To translate the single trial decision rule across trials, one needs to search for the unbiased response criterion that gives the highest d’ between the two curves. For each asynchrony, the probability of “sound first” responses, after having identified such optimal decision rule across trials, is calculated as the sum of the two areas below the visual posterior on the left of the criterion (Hits) and below the audio posterior on the right of the criterion (CR). (B) The probability values of “sound first” responses obtained from the model for different SOAs are analyzed using the Spearman-Kärber method for participants’ responses (see Methods).