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Information Geometry
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.
Mathematical Reviews
None
The Life of Ludwig van Beethoven (Complete)
If for no other reasons than because of the long time and monumental patience expended upon its preparation, the vicissitudes through which it has passed and the varied and arduous labors bestowed upon it by the author and his editors, the history of Alexander Wheelock Thayer’s Life of Beethoven deserves to be set forth as an introduction to this work. His work it is, and his monument, though others have labored long and painstakingly upon it. There has been no considerable time since the middle of the last century when it has not occupied the minds of the author and those who have been associated with him in its creation. Between the conception of its plan and its execution there lies a p...
