Multimodal integration can be determined by the weighted average of the inputs of each modality ( Ernst and Banks, 2002 Alais and Burr, 2004 Klink et al., 2011 Tomassini et al., 2011 Rohe and Noppeney, 2015a, b, 2018 Vercillo and Gori, 2015 Rohe et al., 2019). Investigating multisensory integration reveals how we perceive our world precisely in daily life. Previous studies have suggested the functional importance of such multisensory integration that induced more precise perception rather than unisensory perception ( Ernst and Banks, 2002 Alais and Burr, 2004 Burr et al., 2009 Hartcher-O’Brien et al., 2014 Murai and Yotsumoto, 2018). These illusions result from the integration of spatial or temporal information of visual and auditory modalities. Similarly, this illusion is also found in the temporal domain, as the temporal ventriloquism effect, in which the perceived timing of a visual stimulus is drawn to the timing of the auditory stimulus ( Klink et al., 2011 Vidal, 2017). For example, the ventriloquism effect is the illusory percept, where the perceived location of an auditory stimulus is influenced by the location of the simultaneously presented visual stimulus ( Battaglia et al., 2003 Alais and Burr, 2004). However, integrated multimodal perception may not reflect the true reality. Our perception results from receiving multimodal inputs from one’s surroundings and integrating these inputs as one. Our models can be extended to investigate the neural basis and effects of other sensory modalities in duration integration. These behavioral and modeling results suggest the following: (1) the perceived duration of visual and auditory stimuli is influenced by which modality the participants attended to when we control for the confounding effect of onset–offset timing of stimuli, and (2) the increase of the weight by attention affects the duration integration, even when the effect of stimulus reliability is controlled. In addition, to examine whether auditory dominance results from the higher reliability of auditory stimuli, we applied another models to consider the stimulus reliability. To further investigate the process of duration integration of the two modalities, we applied Bayesian hierarchical modeling, which enabled us to define a flexible model in which the multisensory duration is represented by the weighted average of each sensory modality. Contrary to the attention-independent auditory dominance reported in previous studies, we found that the perceived duration of the simultaneous flicker and flutter presentation depended on which modality the participants attended. The participants were asked to attend either visual, auditory, or both modalities. Since the duration of a visual flicker and auditory flutter tends to be perceived as longer than and shorter than its physical duration, respectively, we used the 10 Hz visual flicker and auditory flutter with the same onset and offset timings but different perceived durations. In the present study, we aimed to investigate the effect of attention on duration integration using visual and auditory stimuli of the same duration.
In these studies, auditory dominance was assessed using visual and auditory stimuli with different durations whose timing of onset and offset would affect perception. However, for duration perception, it has been shown that when duration information from visual and auditory modalities is integrated, the perceived duration of the visual stimulus leaned toward the duration of the auditory stimulus, irrespective of which modality was attended. Generally, such integration is influenced by the modality that we attend to. We constantly integrate multiple types of information from different sensory modalities.