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Recently, it has been shown that visual perception can be radically altered by signals of other modalities. For example, when a single flash is accompanied by multiple auditory beeps, it is often perceived as multiple flashes. This effect is known as the sound-induced flash illusion. In order to investigate the principles underlying this illusion, we developed an ideal observer (derived using Bayes' rule), and compared human judgements with those of the ideal observer for this task. The human observer's performance was highly consistent with that of the ideal observer in all conditions ranging from no interaction, to partial integration, to complete integration, suggesting that the rule used by the nervous system to decide when and how to combine auditory and visual signals is statistically optimal. Our findings show that the sound-induced flash illusion is an epiphenomenon of this general, statistically optimal strategy.