Measuring multisensory integration in reaction time: the relative entropy approach

A classic definition of multisensory integration (MI) has been proposed as ``the presence of a (statistically) significant change in the response to a cross-modal stimulus complex compared to unimodal stimuli''. However, this general definition did not result in a broad consensus on how to quantify the amount of MI in the context of reaction time (RT). In this brief note, we argue that numeric measures of reaction times that only involve mean or median RTs do not uncover the information required to fully assess the effect of multisensory integration. We suggest instead novel measures that include the entire RT distributions functions. The central role is played by relative entropy (aka Kullback-Leibler divergence), a statistical concept in information theory, statistics, and machine learning to measure the (non-symmetric) distance between probability distributions. We provide a number of theoretical examples, but empirical applications and statistical testing are postponed to later study.