A statistical model for binocular rivalry

A probabilistic model is presented for the phase durations in binocular rivalry experiments. The hypothetical construct of inhibition or reaction inhibition is used to account for the length of the successive phases of left-eye dominance and right-eye dominance. In accordance with Hull's Postulate X.B. it is assumed that the inhibition increases linearly at rate a1 during periods of left-eye dominance and decreases linearly at rate a0 during periods of right-eye dominance. Two different versions of the proposed model are presented: the beta and the Bessel inhibition models. Inhibition fluctuates between the boundaries 0 and 1 in the beta inhibition model and between -infinity and +infinity in the Bessel inhibition model. The transition rates lambda1(t) for switches from a state of left-eye dominance to a state of right-eye dominance, and lambda0(t) for switches from a state of right-eye dominance to a state of left-eye dominance depend on inhibition: lambda1(t)=l1 (Y(t)), lambda0(t)=l0(Y(t)), where l1 is a non-decreasing function and l0 is a non-increasing function. In the beta inhibition model l1(y)=c1/(1 - y) and l0(y)=c0/y. In the Bessel inhibition model l1(y)=u1e(y) and l0(y)=u0/e(y). Special attention is given to the derivation of the expectation of the stationary phase durations.