Local information geometry for statistical analysis of high-order binary Markov chains - Voloshko, Valeriy A. (Journal of the Belarusian State University. Mathematics and Informatics, 2026)
At the 14th International conference «Computer data analysis and modelling: stochastics and data analysis» the author presented some new results on asymptotic properties of statistics derived from purely random (uniformly distributed) binary sequence of increasing length. These results are obtained by methods of information geometry applied to manifolds of Markov probability distributions on the set of infinite binary sequences. In this paper the underlying information-geometric theory and the technics of proofs are describe in more detail. By few examples, it is shown how finding probabilistic and statistical properties comes down to geometric and combinatorial computations.
Keywords: information geometry; tangent space; asymptotic distribution; binary sequence; Markov manifold