Abstract

COJ Technical & Scientific Research

A Brief Review of Publications on the Differential Geometry of Statistical Manifolds

  • Open or CloseSergey Stepanov*1,2 and Josef Mikeš3

    1 All Russian Institute for Scientific and Technical Information of the Russian Academy of Sciences, Russia

    2 Finance University under the Government of the Russian Federation, Russia

    3 Palacky University, Czech Republic

    *Corresponding author: Sergey Stepanov, All Russian Institute for Scientific and Technical Information of the Russian Academy of Sciences, Finance University under the Government of the Russian Federation, Moscow, Russia

Submission: November 14, 2019; Published: January 08, 2020

Abstract

We present here a brief review of papers and monographs on the differential geometry of statistical manifolds. We do not pretend to the exhaustive completeness of our review. The review is related to the publication of another monograph Ay N, Jost J, Le H. V, Schwachhofer L, Information Geometry, Vol. 64 of a Series of Modern Surveys in Mathematics, Springer Int. Publ. AG, 2017. We recall that Information geometry studies invariant properties of a family of probability distributions and can be applied to various problems in science. Statisticians use statistical models to derive inferences; they use families of probability distributions which form, in most cases, a finite dimensional manifold which in information geometry is called a statistical manifold. Many authors contributed to the development of information geometry or, in other words, geometrical theory of statistics.

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