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Fisher information and . . .
, 2012
"... Fisher information is an important concept in statistical estimation theory and information theory, but it has received relatively little consideration in statistical physics. In order to rectify this oversight, in this brief note I will review the correspondence between Fisher information and fluct ..."
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Fisher information is an important concept in statistical estimation theory and information theory, but it has received relatively little consideration in statistical physics. In order to rectify this oversight, in this brief note I will review the correspondence between Fisher information
Covariance and Fisher information in quantum mechanics
, 2002
"... Variance and Fisher information are ingredients of the CramerRao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and Fisher information. In this approach we show t ..."
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Cited by 30 (14 self)
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Variance and Fisher information are ingredients of the CramerRao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of variance and Fisher information. In this approach we show
Fisher information in quantum statistics
 J. Phys. A
"... number to define, meaningfully, a metric on the set of all possible states of a given quantum system. They showed that the quantum information is nothing else than the maximal Fisher information in a measurement of the quantum system, maximized over all possible measurements. Combining this fact wit ..."
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Cited by 15 (2 self)
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number to define, meaningfully, a metric on the set of all possible states of a given quantum system. They showed that the quantum information is nothing else than the maximal Fisher information in a measurement of the quantum system, maximized over all possible measurements. Combining this fact
FISHER INFORMATION IN ORDER STATISTICS
"... We provide a brief survey of results on Fisher information (FI) contained in order statistics and discuss some applications to inference. We specifically consider FI in a single order statistic and in a collection of order statistics, and present finite sample and asymptotic results. We discuss rese ..."
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Cited by 1 (0 self)
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We provide a brief survey of results on Fisher information (FI) contained in order statistics and discuss some applications to inference. We specifically consider FI in a single order statistic and in a collection of order statistics, and present finite sample and asymptotic results. We discuss
Inequalities for quantum Fisher information
 Amer. Math. Soc
"... In the paper [16] Luo proved an inequality relating the WignerYanase information and the SLDinformation. In this paper we prove that Luo’s inequality is a particular case of a general inequality which holds for any regular quantum Fisher information. Moreover we show that this general inequality i ..."
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Cited by 4 (2 self)
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In the paper [16] Luo proved an inequality relating the WignerYanase information and the SLDinformation. In this paper we prove that Luo’s inequality is a particular case of a general inequality which holds for any regular quantum Fisher information. Moreover we show that this general inequality
Physics from Fisher Information
"... The aim of this book is to show that information is at the root of all fields of science. These fields may be generated by use of the concept of ''extreme physical information,'' or EPI. The physical information is defined to be the loss of Fisher information that is incurred in ..."
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The aim of this book is to show that information is at the root of all fields of science. These fields may be generated by use of the concept of ''extreme physical information,'' or EPI. The physical information is defined to be the loss of Fisher information that is incurred
Fisher Information in Weighted Distributions
, 1998
"... Standard inference procedures assume a random sample from a population with density f # (x) for estimating the parameter #. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) # 0, and constructe ..."
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Cited by 1 (0 self)
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, and constructed a weighted distribution with a density f w # (x) that is proportional to w(x)f # (x). In this paper, we assume that f # (x) belongs to an exponential family, and study the Fisher information about # in observations obtained from some commonly arising weighted distributions: (i)thek th order
Fisher Information Test of Normality
, 1998
"... An extremal property of normal distributions is that they have the smallest Fisher Information for location among all distributions with the same variance. A new test of normality proposed by Terrell (1995) utilizes the above property by finding that density of maximum likelihood constrained on havi ..."
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Cited by 1 (0 self)
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An extremal property of normal distributions is that they have the smallest Fisher Information for location among all distributions with the same variance. A new test of normality proposed by Terrell (1995) utilizes the above property by finding that density of maximum likelihood constrained
Dynamics of the Fisher Information Metric
, 2004
"... We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional J[g µν (θ i)], where g µν (θ i) is the Fisher metric. We postulate that this functional of the dynamical variable g µν (θ i) is stationary ..."
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) is stationary with respect to small variations of these variables. Our approach enables a dynamical approach to Fisher information metric. It allows to impose symmetries on a statistical system in a systematic way. This work is mainly motivated by the entropy approach to nonmonotonic reasoning.
Results 1  10
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241,597