Testing for selectivity in the dependence of random variables on external factors

Random variables A and B, whose joint distribution depends on factors (x,y), are selectively influenced by x and y, respectively, if A and B can be represented as functions of, respectively, (x,S_A,C) and (y,S_B,C), where S_A,S_B,C are stochastically independent and do not depend on (x,y). Selective influence implies selective dependence of marginal distributions on the respective factors: thus no parameter of A may depend on y. But parameters characterizing stochastic interdependence of A and B, such as their mixed moments, are generally functions of both x and y. We derive two simple necessary conditions for selective dependence of (A,B) on (x,y), which can be used to conduct a potential infinity of selectiveness tests. One condition is that, for any factor values x,x^′ and y,y^′,

s_xy≤s_xy^′+s_x^′y^′+s_x^′y,     

Corrigendum to “From Poisson shot noise to the integrated Ornstein-Uhlenbeck process: Neurally principled models of information accumulation in decision-making and response time” [J. Math. Psychol. 54 (2010) 266-283]

The Corrigendum reports an error in the derivation by Smith (2010) of the moment generating function for a random-amplitude, time-inhomogeneous, Poisson shot noise process. The correct derivation of the moment generating function is given, together with corrected expressions for the moments.