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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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Informative Geometry of Probability Spaces [PDF]
, 1984 The paper deals with the geometrical properties that are induced by the local information content and structures of the parameter space of probability distributions. In this investigation the Rao distance which is the geodesic distance induced by the differential metric associated with the Fisher matrix of the parameter space, plays a major role ...
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Failures of information geometry
AIP Conference Proceedings, 2015Information H is a unique relationship between probabilities, based on the property of independence which is central to scientific methodology. Information Geometry makes the tempting but fallacious assumption that a local metric (conventionally based on information) can be used to endow the space of probability distributions with a preferred global ...
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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 ...
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Critique of information geometry
AIP Conference Proceedings, 2014As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to ...
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The geometry of informational extensions
Automation and Remote Control, 2009The paper studies strategy spaces in all possible informational extensions of a game with the natural metric. We show that all these extensions can be considered subspaces of a single space corresponding to a special quasi-informational extension that has a clear meaningful interpretation.
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Information Geometry of Thermodynamics
1988It is shown that a set of probability distributions (statistical states, states) of a nonequilibrium thermodynamical system can be equipped with the structure of a Finsler space. The Lagrange function L of the space is defined by means of the relative entropy between states. The time variable is specified as an additional position variable by requiring
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The Development of Informal Geometry
National Mathematics Magazine, 1943E. R. Breslich, Robert Coleman join(
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