Methods of Information GeometryInformation geometry provides the mathematical sciences with a fresh framework of analysis. This book presents a comprehensive introduction to the mathematical foundation of information geometry. It provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, and convex analysis. |
Contents
Elementary differential geometry | 1 |
The geometric structure of statistical models | 25 |
Dual connections | 51 |
Statistical inference and differential geometry | 81 |
The geometry of time series and linear systems | 115 |
Multiterminal information theory and statistical inference | 133 |
Information geometry for quantum systems | 145 |
Miscellaneous topics | 167 |
| 181 | |
Bibliography | 187 |
| 203 | |
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Common terms and phrases
a-connections addition Amari applied arbitrary assume asymptotically components condition connection consider consisting constant contained convex coordinate system corresponding covariance curvature curve defined definition denote derivative determined differential geometry direction discussion divergence dual dualistic structure dually flat element Equation equivalent error estimation theory Example exists exponential family expressed finite Fisher information Fisher metric function given hence holds induced inference information geometry inner product introduced invariant linear manifold mapping Mathematics matrix mean measurement natural necessary normal Note observed obtain operator orthogonal parallel parameter particular positive possible probability distributions problem properties quantum relation represented respect result Riemannian satisfies simply space statistical model structure submanifold sufficient suppose symmetric tangent space tangent vector tensor Theorem theory tion transformation translation vector fields written