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In the solution proposed by Cannon 9, the Gaussian posterior updates continuously between events at every time step, and additionally updates after event observations. At any time t, the sufficient statistics are denoted by the mean μt and variance Vt. If an event occurs at time t, these values (left-hand limits) are revised to μt+ and Vt+ (right-hand limits). Cannon’s solution is a generalized Kalman-Bucy filter with Poisson observation noise 9.
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We demonstrated the systematic bias incurred when tracking a patterned rhythm without a corresponding pattern of expectations 5; and conversely the perceptual bias towards specific rhythmic patterns during iterated reproduction. In doing so, we related the implicit pattern inference in pPIPPET to empirical data on perceptual categorization of rhythms 1. These behaviors emerge naturally when entrainment is described as a process of Bayesian inference, PIPPET 9, where precise phase-based temporal expectations are optimized using prior expectations for different rhythmic patterns.
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