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This study provides a normative theory for how Bayesian causal inference can be implemented in neural circuits. In both cognitive processes such as causal reasoning and perceptual inference such as cue integration, the nervous systems need to choose different models representing the underlying causal structures when making inferences on external stimuli. In multisensory processing, for example, the nervous system has to choose whether to integrate or segregate inputs from different sensory modalities to infer the sensory stimuli, based on whether the inputs are from the same or different sources. Making this choice is a model selection problem requiring the computation of Bayes factor, the ratio of likelihoods between the integration and the segregation models. In this paper, we consider the causal inference in multisensory processing and propose a novel generative model based on neural population code that takes into account both stimulus feature and stimulus reliability in the inference. In the case of circular variables such as heading direction, our normative theory yields an analytical solution for computing the Bayes factor, with a clear geometric interpretation, which can be implemented by simple additive mechanisms with neural population code. Numerical simulation shows that the tunings of the neurons computing Bayes factor are consistent with the "opposite neurons" discovered in dorsal medial superior temporal (MSTd) and the ventral intraparietal (VIP) areas for visual-vestibular processing. This study illuminates a potential neural mechanism for causal inference in the brain. 

Our brain perceives the world by exploiting multisensory cues to extract information about various aspects of external stimuli. The sensory cues from the same stimulus should be integrated to improve perception, and otherwise segregated to distinguish different stimuli. In reality, however, the brain faces the challenge of recognizing stimuli without knowing in advance the sources of sensory cues. To address this challenge, we propose that the brain conducts integration and segregation concurrently with complementary neurons. Studying the inference of heading-direction via visual and vestibular cues, we develop a network model with two reciprocally connected modules modeling interacting visual-vestibular areas. In each module, there are two groups of neurons whose tunings under each sensory cue are either congruent or opposite. We show that congruent neurons implement integration, while opposite neurons compute cue disparity information for segregation, and the interplay between two groups of neurons achieves efficient multisensory information processing.