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Method for estimating discharge, hydraulic depth, and mean velocity in rivers through spatial interpolation of at-a-station hydraulic geometry in data- scarce regions. [PDF]
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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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Information geometry and statistical manifold
Chaos, Solitons & Fractals, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdel-All, Nassar H. +2 more
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INFORMATION GEOMETRY AND PHASE TRANSITIONS
Recent Progress in Many-Body Theories, 2006We present, from an information theoretic viewpoint, an analysis of phase transitions and critical phenomena in quantum systems. Our study is based on geometrical considerations within the Riemannian space of thermodynamic parameters that characterize the system.
Portesi, Mariela +2 more
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Information geometry of Boltzmann machines
IEEE Transactions on Neural Networks, 1992A Boltzmann machine is a network of stochastic neurons. The set of all the Boltzmann machines with a fixed topology forms a geometric manifold of high dimension, where modifiable synaptic weights of connections play the role of a coordinate system to specify networks. A learning trajectory, for example, is a curve in this manifold.
S, Amari, K, Kurata, H, Nagaoka
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Information Geometry for Symmetric Diffusions
Potential Analysis, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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