Behavioral measures of multisensory integration: bounds on bimodal detection probability

One way to test and quantify multisensory integration in a behavioral paradigm is to compare bimodal detection probability with bounds defined by some combination of the unimodal detection probabilities. Here we (1) improve on an upper bound recently suggested by Stevenson et al. (Brain Topogr 27(6):707-730, 2014), (2) present a lower bound, (3) interpret the bounds in terms of stochastic dependency between the detection probabilities, (4) discuss some additional assumptions required for the validity of any such bound, (5) suggest some potential applications to neurophysiologic measures, and point out some parallels to the 'race model inequality' for reaction times.