Interaction information and Markov chain

Seiji Takano

Journal of Multivariate Analysis, 1973, vol. 3, issue 1, 93-101

Abstract: The problem of multivariate information analysis is considered. First, the interaction information in each dimension is defined analogously according to McGill [4] and then applied to Markov chains. The property of interaction information zero deeply relates to a certain class of weakly dependent random variables. For homogeneous, recurrent Markov chains with m states, m >= n >=3, the zero criterion of n-dimensional interaction information is achieved only by (n - 2)-dependent Markov chains, which are generated by some nilpotent matrices. Further for Gaussian Markov chains, it gives the decomposition rule of the variables into mutually correlated subchains.

Keywords: Interaction; information; Markov; chain; M-dependence; multivariate; information; analysis; information; theory (search for similar items in EconPapers)
Date: 1973
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