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Topic: Fisher information metric

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Information geometry

Fisher information

Information theory

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	Fisher information - Wikipedia, the free encyclopedia
		Fisher information is thought of as the amount of information that an observable random variable carries about an unobservable parameter θ upon which the probability distribution of X depends.
		The Fisher information is thus the expectation of the square of the score.
		Information may thus be seen to be a measure of the "sharpness" of the support curve near the maximum likelihood estimate of θ.
	en.wikipedia.org /wiki/Fisher_information (673 words)

	Fisher information - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-09-07)
		Fisher information is thought of as the amount of information that an observable random variable carries about an unobservable parameter $\theta$ upon which the probability distribution of $X$ depends.
		Information may thus be seen to be a measure of the "sharpness" of the support curve near the maximum likelihood estimate of $\theta$ .
		In case the parameter $\theta$ is vector-valued, the information is a positive-definite matrix, which defines a metric on the parameter space; consequently differential geometry is applied to this topic.
	www.arikah.net /encyclopedia/Fisher_information (876 words)

	Encyclopedia: Fisher information
		Fisher information is thought of as the amount of information that an observable random variable carries about an unobservable parameter
		Information theory is a branch of the mathematical theory of probability and mathematical statistics that quantifies the concept of information.
		In statistics, the CramÃ©r-Rao inequality, named in honor of Harald CramÃ©r and Calyampudi Radhakrishna Rao, states that the reciprocal of the Fisher information,, of a parameter, is a lower bound on the variance of an unbiased estimator of the parameter (denoted).
	www.nationmaster.com /encyclopedia/Fisher-information (1373 words)

	Fisher information -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-09-07)
		Fisher information is thought of as the amount of (A message received and understood) information that an observable (A variable quantity that is random) random variable carries about an unobservable parameter upon which the (additional info and facts about probability distribution) probability distribution of depends.
		Information may thus be seen to be a measure of the "sharpness" of the support curve near the (additional info and facts about maximum likelihood estimate) maximum likelihood estimate of.
		In case the parameter is vector-valued, the information is a positive-definite matrix, which defines a metric on the parameter space; consequently (additional info and facts about differential geometry) differential geometry is applied to this topic.
	www.absoluteastronomy.com /encyclopedia/F/Fi/Fisher_information.htm (850 words)

	Information geometry - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-09-07)
		In mathematics and especially in statistical inference, information geometry is the study of probability and information by way of differential geometry.
		Information geometry is based primarily on the Fisher information metric:
		Thus, if a point in information space represents the state of a system, then the trajectory of that point will, on average, be a random walk through information space, i.e.
	www.arikah.net /encyclopedia/Information_geometry (339 words)

	Fisher information (Site not responding. Last check: 2007-09-07)
		In statistics the Fisher information I (θ) thought of as the amount of information that an observable random variable carries about an unobservable parameter θ which the probability distribution of X depends is the variance of the score.
		The Fisher information is thus the of the square of the score.
		Information may thus be seen to a measure of the "sharpness" of the curve near the maximum likelihood estimate of θ.
	www.freeglossary.com /Fisher_information (747 words)

	Information geometry (Site not responding. Last check: 2007-09-07)
		In mathematics, information geometry is the study of probability and information by way of differentialgeometry.
		Information geometry is based primarily on the Fisher information metric :
		Thus, if a point in information space represents the state of a system, then the trajectory of that point will, on average, bea random walk through information space, i.e.
	www.therfcc.org /information-geometry-34392.html (274 words)

	Fisher information metric - Wikipedia, the free encyclopedia
		In mathematics, in information geometry, the Fisher information metric is a metric tensor for a statistical differential manifold.
		It can be used to calculate the informational difference between measurements.
		Which can be thought of intuitively as: "The distance between two points on a statistical differential manifold is the amount of information between them, i.e.
	en.wikipedia.org /wiki/Fisher_information_metric (135 words)

	Informasi Fisher - Wikipédia
		Dina statistik, informasi Fisher I(θ), nyaeta information random variable nu bisa diobservasi mawa kanyaho ngeunaan parameter nu teu ka observasi θ nu gumantung kana probability distribution X, ngarupakeun score varian.
		Informasi Fisher saterusna ngarupakeun ekspektasi kuadrat tina skor.
		Konsep ieu dipake keur ngahargaan ka ahli genetis jeung statistikawan Ronald Fisher.
	su.wikipedia.org /wiki/Fisher_information (463 words)

	Fisher information (Site not responding. Last check: 2007-09-07)
		In statistics, the Fisher information I(θ),thought of as the amount of information that an observable random variable carries about an unobservable parameter θ upon which the probability distribution of X depends, isthe variance of the score.
		Information may thusbe seen to be a measure of the "sharpness" of the support curve near the maximum likelihood estimate of θ.
		In case the parameter θ is vector valued, the information is a positive-definite matrix, which defines a metric on theparameter space; consequently differential geometry isapplied to this topic.
	www.therfcc.org /fisher-information-12902.html (511 words)

	Brainstorms: Conceding Too Much
		The variational information does not take into account the metric structure of the underlying probability space and therefore suggests far more discontinuity than is actually present in probability paths.
		It's therefore necessary to factor in the metric structure of the underlying probability space, and I argue this is properly done using the Kantorovich-Wasserstein metric.
		Fisher information, which is the basis for a lot of current research in information geometry and which Roy Frieden in the last five years has shown provides a framework for understanding most of physics, was developed by Ronald Fisher in 1925 and is now 79 years old.
	www.iscid.org /boards/ubb-get_topic-f-6-t-000537.html (941 words)

	OPTI 529
		Fisher information I as an entropy – the ‘I theorem’.
		The multidimensional Fisher information I form to be used in all physical derivations: the trace of the Fisher information matrix.
		J is an information that is entangled with the phenomenon under measurement.
	www.optics.arizona.edu /Classes/Grad/Opti_529.htm (707 words)

	Fisher information - Term Explanation on IndexSuche.Com
		Information as defined above may be written as : I(\theta)=-E\left[ \frac{\partial^2}{\partial\theta^2} \log f(X;\theta) \right] and is thus the expection of log of the second derivative of ''X'' with respect to ''θ''.
		Information is additive, in the sense that the information gathered by two independent experiments is the sum of the information of each of them: : I_{X,Y}(\theta)=I_X(\theta)+I_Y(\theta).
		The Cramér-Rao_inequality states that the reciprocal of the Fisher information is a lower bound on the variance of any unbiased estimator of θ.
	www.indexsuche.com /Fisher_information.html (581 words)

	Fisher information - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-09-07)
		In statistics, the Fisher information I(θ), thought of as the amount of information that an observable random variable carries about an unobservable parameter θ upon which the probability distribution of X depends, is the variance of the score.
		Because the expectation of the score is zero, this may be written as
		This concept is named in honor of the geneticist and statistician Ronald Fisher.
	www.encyclopedia-online.info /Fisher_information (552 words)

	Fisher information (Site not responding. Last check: 2007-09-07)
		A sufficiency paradox: an insufficient statistic preserving the Fisher information.
		The FIM is a d by d and symmetric matrix.
		Fisher's rapid lumber and short-cut calculator: Being a simplified method of figuring lumber and other useful short-cuts...
	hallencyclopedia.com /Fisher_information (902 words)

	fisher dynamics (Site not responding. Last check: 2007-09-07)
		The geometry of the Fisher selection dynamics The geometry of the Fisher selection dynamics We study the Fisher model describing natural selection in a population with a diploid structure of a genome by differential- geometric methods.
		Dynamics of the Fisher Information Metric Dynamics of the Fisher Information Metric We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a...
		Applicability of the Fisher Equation to Bacterial Population Dynamics Applicability of the Fisher Equation to Bacterial Population Dynamics The applicability of the Fisher equation, which combines diffusion with logistic nonlinearity, to...
	www.nopump.com /articles/69/fisher-dynamics.html (966 words)

	An Introduction to Markov Chain Monte Carlo
		However, if a parametric model is available for the data and all the prior information (besides the knowledge of this parametric model) is contained in the initial value of the parameter, then the entropic priors, as defined by equation (1), provide invariant assignments of prior probabilities with desirable properties.
		In information theoretic terms, it is said to measure the mean information per observation for discrimination in favor of P and against Q when sampling from P. In stronger information theoretic language, it is the expected amount of information transmitted by the message: "The information source has been moved from Q to P".
		The matrix of this quadratic form is known as the Fisher information matrix and the induced Riemannian metric is known as the information metric
	omega.albany.edu:8008 /entpriors.html (5178 words)

	Fisher information (Site not responding. Last check: 2007-09-07)
		Information may thus be seen to be a measure of the "sharpness" of the support curve near the maximum likelihood estimate of
		The information provided by a sufficient statistic is same as that of the sample
		The first line is just the definition of information; the second uses the fact that the information contained in a sufficient statistic is the same as that of the sample itself; the third line just expands the log term (and drops a constant), the fourth and fifth just differentiation with respect to
	www.worldhistory.com /wiki/F/Fisher-information.htm (779 words)

	Fisher Information (Site not responding. Last check: 2007-09-07)
		Fisher interviewed Couture on July 20, 52 days after the shooting.
		More information about the official water agreement can be accessed by the public at...
		Remel, a unit of Fisher Biosciences, is a global provider of a wide range of high...
	www.wikiverse.org /fisher-information (673 words)

	Machine Learning (Theory) » Loss Functions for Discriminative Training of Energy-Based Models (Site not responding. Last check: 2007-09-07)
		The Fisher metric is a local approximation to the KL-divergence.
		I’m not sure I’d agree with the notion that the fisher metric is a local approximation to the KL-divergence: If you look either at Cencov or at Amari’s work, it seems that the Fisher metric is the “prime notion”.
		Moreover, the Hellinger distance is the “natural” geodesic associated with the Fisher information.
	hunch.net /index.php?p=26 (1281 words)

	Geometries of Quantum States - Petz, Sudar (ResearchIndex) (Site not responding. Last check: 2007-09-07)
		Abstract: The quantum analogue of the Fisher information metric of a probability simplex is searched and several Riemannian metrics on the set of positive definite density matrices are studied.
		All stochastically monotone Riemannian metrics are characterized by means of operator monotone functions and it is...
		1 An extended Cencov charecterization of the information metri..
	citeseer.ist.psu.edu /petz96geometries.html (680 words)

	Quantum computation: theory and implementation (Site not responding. Last check: 2007-09-07)
		It is noted that very little synthesis has been performed on the information here presented; most of the paragraphs are summaries of various different sources, assembled for easy reference and as an aid to thinking.
		This is essential for a proper understanding of quantum information theory, and to an understanding of quantum measurement.
		which says that the information gotten by examining the value of a random variable can be obtained by first determining whether it is in a certain set of values, then determining what member of the set it corresponds to (Fuc96).
	www.stanford.edu /~eboyden3/mengthesis/thesis1.htm (3264 words)

	Information Geometry
		One very nice thing about information geometry is that it gives us very strong tools for proving results about statistical models, simply by considering them as well-behaved geometrical objects.
		Thus, for instance, it's basically a tautology to say that a manifold is not changing much in the vicinity of points of low curvature, and changing greatly near points of high curvature.
		Kazushi Ikeda, "Information Geometry of Interspike Intervals in Spiking Neurons",
	bactra.org /notebooks/info-geo.html (713 words)

	MaxEnt 2000 abstracts.htm (Site not responding. Last check: 2007-09-07)
		In both cases the input information for the procedure are M expectation values of the state one is trying to infer.
		Information content of the binding sites is evaluated as a measure of uncertainty of what base to expect in another LexA binding site in the form of Shannon's entropy in statistics, where is the frequency of base B at position L and the sum is taken over all bases.
		Information Independence If a statement is refined by several new symbols, it should be possible to state that they are information independent, so that knowledge of one does not affect the plausibility of the other.
	www.nd.edu /~adjafari/MaxEnt2000/htm/abstracts.htm (17402 words)

	ANC WORKSHOP
		The results are interpretable that the hemifield division of information is very precise (dividing a single character) and that the effects of the division extend sufficiently far into the processing for the gender of the reader to have an effect.
		Where information concerning molecular components is incomplete or masked by noise (as it usually is), strategies must be developed to identify those genes/proteins involved.
		It's undeniable the ability of the nervous system to perform temporal information processing: tasks like distinguishing two brief tone pulses separated by either 50 or 100 ms, coordinating arm movements or playing music are examples of temporal pattern interpretation and control of temporal pattern production that remain poorly understood in terms of their underlying mechanisms.
	www.anc.ed.ac.uk /events/ancwkshp_past.html (18498 words)

	Department of Mathematics & Statistics \| University of Guelph
		Description: Classical information geometry concerns the study of families of probability distributions.
		Parametric models are viewed as finite dimensional manifolds and probabilistic concepts acquire a geometric meaning, such as the Fisher information metric, which is regarded as a Riemannian metric.
		The extension to infinite dimensional manifolds of states on von Neumann algebras is technically challenging in part due to the lack of a well developed theory of Quantum Orlicz spaces.
	www.mathstat.uoguelph.ca /?action=event&id=225 (175 words)

	Re: Fisher Information - Frieden unification Of Physics
		IIRC, the Fisher information matrix appears as the metric tensor, and that then the Guassian curvature (for a two parameter model) is some kind of entropy.
		On the right side, the Rokhlin metric is H(A/B) + H(B/A) (sum of conditional entropies) which is a true metric if you mod out by zero entropy stuff, much like what you do in forming L^p spaces.
		I have alot of background in information theory and math (much less in physics), including a full year graduate course in functional analysis.
	www.lns.cornell.edu /spr/1999-10/msg0018767.html (1357 words)

	Information Geometry (Site not responding. Last check: 2007-09-07)
		There is a natural flow of information among family members in both academic...
		Whether comparatively amorphous or hinged at geometry, the images are slight but...
		details of Dr. Khan's offer made it clear that the sensitive information was probably...
	www.wikiverse.org /information-geometry (417 words)

	Fisher Information (Site not responding. Last check: 2007-09-07)
		It looks very Fisher-Price and its screen has frozen but it would be churlish to nitpick â“ this piece of technology really could make a difference and is...
		systems of neurons operate as circuits, collectively processing information that ultimately...
		For more information call the Como at 535-2476.
	fisher-information.wikiverse.org (663 words)

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