Towards an information-theoretic model of the Allison mixture stochastic process

The Allison mixture is a random process formed by stochastically switching between two random and uncorrelated input processes. Unintuitively, these samples—independent prior to being drawn—can acquire dependence as a result of the sampling process. It has previously been shown that correlation can occur subject to certain conditions, however in general dependence does not imply correlation. In this paper we provide an initial information-theoretic analysis of the Allison mixture, and derive the autoinformation function of its sampling process as the first step towards a fuller information-theoretic analysis of its output. (special issue on unsolved problems of noise in physics, biology and technology)