DIFFERENTIAL METRICS IN PROBABILITY SPACES
Jacob Burbea
C. Radhakrishna Rao
Abstract: In this paper we discuss the construction of differential metrics in probability
spaces through entropy functional and examine their relations with the information metric
introduced by Rao using the Fisher information matrix in the statistical problem of
classification and discrimination, and the classical Bergman metric. It is suggested that the
scalar and Ricci curvatures associated with the Bergman information metric may yield results
in statistical inference analogous to those of Efron using the Gaussian curvature.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -