Methods of information geometry
Amari, Shun-ichi
Methods of information geometry - Providence: American Mathematical Society, 2000. - x, 206p.; pbk; 25cm - Translations of mathematical monographs; Vol. 191 .
includes bibliography and index
Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the α-connections. The duality between the α-connection and the (−α)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective.
https://bookstore.ams.org/mmono-191
9780821843024
Mathematical statistics
Geometry
Differential
geometric structure
probability distribution
information theory
quantum mechanics
519.5 / AMA
Methods of information geometry - Providence: American Mathematical Society, 2000. - x, 206p.; pbk; 25cm - Translations of mathematical monographs; Vol. 191 .
includes bibliography and index
Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the α-connections. The duality between the α-connection and the (−α)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective.
https://bookstore.ams.org/mmono-191
9780821843024
Mathematical statistics
Geometry
Differential
geometric structure
probability distribution
information theory
quantum mechanics
519.5 / AMA
