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Japanese Journal of Mathematics, 2021
SummaryStatistical inference is constructed upon a statistical model consisting of a parameterised family of probability distributions, which forms a manifold. It is important to study the geometry of the manifold. It was Professor C. R. Rao who initiated information geometry in his monumental paper published in 1945.
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SummaryStatistical inference is constructed upon a statistical model consisting of a parameterised family of probability distributions, which forms a manifold. It is important to study the geometry of the manifold. It was Professor C. R. Rao who initiated information geometry in his monumental paper published in 1945.
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2017
This chapter investigates probability distributions on a finite sample space and takes advantage of the more elementary nature of this setting. There are two complementary ways to view a probability distribution. One consists in viewing it as (positive) measure with total mass 1.
Ay, Nihat +3 more
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This chapter investigates probability distributions on a finite sample space and takes advantage of the more elementary nature of this setting. There are two complementary ways to view a probability distribution. One consists in viewing it as (positive) measure with total mass 1.
Ay, Nihat +3 more
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Information Geometry and Statistics
2017We apply the functional analytical and differential geometric results of the preceding chapters to the field of statistics and obtain very general versions of the basic classical results. In a narrower sense, the term statistic refers to a mapping from a given sample space Ω to another Ω′, and it is called sufficient for a parametric family, if the ...
Ay, Nihat +3 more
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Fields of Application of Information Geometry
20171.Complexity measures can be geometrically built by using the information distance (Kullback–Leibler divergence) from families with restricted statistical dependencies. The Pythagorean geometry developed in Chaps. 2 and 4 allows us to iterate such constructions, by going to simpler and simpler families and taking—possibly weighted—sums, thereby ...
Ay, Nihat +3 more
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Representational geometry of perceptual decisions in the monkey parietal cortex
Cell, 2021Gouki Okazawa +2 more
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The Geometry of Abstraction in the Hippocampus and Prefrontal Cortex
Cell, 2020Silvia Bernardi +2 more
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Prediction of railroad track geometry change using a hybrid CNN-LSTM spatial-temporal model
Advanced Engineering Informatics, 2023Yun Bai
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Special geometry, Hessian structures and applications
Physics Reports, 2020Gabriel Lopes Cardoso, Thomas Mohaupt
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Review of thermoelectric geometry and structure optimization for performance enhancement
Applied Energy, 2020Samson Shittu +2 more
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