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.