Information Geometry (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) (v. 64)

Penned By Nihat Ay
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Information Geometry (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) (v. 64)

Penned By Nihat Ay
4.85 13,276 Ratings
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Editor's Note:
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.

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Length 420 Pages
Language Eng
Imprint Springer
Released N/A
Identifier (ISBN) 56995372
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Nihat Ay
The Mind Behind the Work
Nihat Ay

Nihat Ay writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. Nihat Ay lives with their spouse and a very vocal rescue cat.

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Carol Lewis
Carol Lewis August 14, 2024
"A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel."
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Jacob Turner March 23, 2024
"A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
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Steven Allen
Steven Allen August 29, 2025
"I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars."
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"Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me."
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"Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall."
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"I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel."
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"I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
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"It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes."
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"A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers."
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"Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
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"Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
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"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author."
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"A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece."
Edward Adams
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"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem."
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"Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
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"A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel."
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"A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre."
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"Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author."
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"A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me."
Susan Lewis
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"Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece."
Barbara Nelson
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"Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre."
Joseph Harris
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"A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre."
Gary Nelson
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"A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall."
Charles Walker
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"Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece."
Nancy Lee
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"A decent, if standard, experience. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty."
Donna Collins
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"Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
Deborah Lewis
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Richard Moore
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"Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading."
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"Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre."
Jacob Collins
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"I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
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Ashley Campbell
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"I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
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"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
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Donald Harris
Donald Harris February 07, 2024
"I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem."
Christopher Evans
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"Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece."
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"Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me."
Gary Miller
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Joseph Diaz
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"Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
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