Comparing Bayesian models for simultaneity judgement with different causal assumptions

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In recent years, Bayesian causal inference has emerged as a computational principle for multisensory integration; it considers the causal relationships of multisensory stimuli and combines stimuli only when they are causally related. Many empirical studies have confirmed the predictions of Bayesian causal inference models and have begun to reveal the neural mechanisms of their computations. However, some studies have suggested that Bayesian causal inference does not always hold, and it is still unclear if Bayesian causal inference is a general computational principle or whether it simply represents a limited range of multisensory integration. Most theoretical and empirical Bayesian causal inference studies have focused on the binary judgement of pairs of multisensory stimuli or sequences of stimuli. One empirical study presented a more complex case with one auditory stimulus and two visual stimuli. In this study, I propose three Bayesian causal models with different causal structures regarding the same scenario. The first model assumes that an auditory stimulus is integrated with a visual stimulus only when they share the same source. During model derivation, I present a hierarchical formulation of causal structural priors in complex situations with multiple number of audio-visual stimuli. The second model assumes that an auditory stimulus is forcibly integrated with one of two visual stimuli. The third model assumes that all three stimuli are forcibly integrated. First, with minimum assumptions, I demonstrated that the full causal model explains existing experimental results better than the other two models. Meanwhile, by introducing another modelling parameter for simultaneity judgement criterion in different experimental conditions, the extended versions of the other two models also described the experimental results almost as accurately as the full causal model. It was confirmed that all three models explain the empirical results of simultaneity judgements of audio-visual stimuli, as well as the enhancement of sensitivity, to some degree. Although these models are difficult to distinguish based on existing data, they provide different interpretations of the underlying mechanisms of empirical findings. Additionally, I demonstrated that these models make qualitatively different predictions, and presented experimental manipulations that can distinguish the models based on the underlying causal structures of multiple multisensory stimuli.

Original languageEnglish
Article number102521
JournalJournal of Mathematical Psychology
Publication statusPublished - 2021 Jun
Externally publishedYes


  • Audio-visual integration
  • Bayesian model
  • Causal inference
  • Simultaneity judgement

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics


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