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	Fisher information - Wikipedia, the free encyclopedia
		The Fisher information is thus the expectation of the squared score.
		Thus Fisher information is the negative of the expectation of the second derivative of the log of f with respect to θ.
		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 (820 words)

	Fisher Information and the Cramer-Rao Bound
		Fisher Information is then a measure of the information content of the measured signal relative to a particular parameter.
		is the Fisher Information matrix of the parameter vector
		that is orthogonal to the Fisher Information of the nuisance parameters, or
	www.colorado.edu /isl/papers/info/node2.html (558 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)

	A Pragmatic Approach to the Design of Population Pharmacokinetic Studies
		The most widely accepted theoretical approach of determining optimal sampling times for PK studies is based on the Fisher information matrix, the elements of which are the negative of the expected values of the second-order partial derivatives of the likelihood.
		A commonly used criterion for determining optimal sampling times is maximization of the determinant of the Fisher information matrix (or, equivalently, minimization of the inverse of the determinant), which is known as D-optimality criterion.
		Information theory suggests that at least 2 sampling times are needed in a single-dose individual subject PK study for the estimation of clearance and volume of a 1-compartment model after IV dose administration.
	www.aapsj.org /view.asp?art=aapsj070241 (6761 words)

	Information Geometry Encyclopedia Article @ Ordinarily.net (Site not responding. Last check: 2007-11-06)
		3 Fisher information metric as a Riemannian metric
		The great statistician Fisher recognized in the 1920s that there is an intrinsic measure of amount of information for statistical estimators.
		The Fisher information matrix was shown by Cramer and Rao to be a Riemannian metric on the space of probabilities, and became known as Fisher information metric.
	www.ordinarily.net /encyclopedia/Information_geometry (851 words)

	Fisher Information
		Information levels I and J are, as we saw, those of the data in the message (the "information sink") and of the source.
		This information is supposed to somehow flow from the unobserved particle to the observed one, "informing" it (or interacting with it, which is why it is called "active") about some property of the unobserved particle (say, its spin state).
		Finally, the information that describes the quality of the observation is, by a requirement of invariance of information to reference frame, the Fisher information for a four-vector measurement.
	www.optics.arizona.edu /Frieden/Fisher_Information.htm (12768 words)

	PlanetMath: Fisher information matrix
		is the design matrix of the regression model.
		In general, the Fisher information meansures how much “information” is known about a parameter
		This is version 10 of Fisher information matrix, born on 2004-07-27, modified 2006-09-23.
	planetmath.org /encyclopedia/InformationMatrix.html (174 words)

	Fisher Information
		For one continuous-valued parameter theta, the Fisher information is defined to be:
		The Fisher information shows how sensitive the likelihood is to the parameter estimate theta.
		The Fisher information is now defined to be the determinant of F(theta).
	www.csse.monash.edu.au /~lloyd/tildeMML/Notes/Fisher.html (670 words)

	Information geometry - Wikipedia, the free encyclopedia
		The main tenet of information geometry is that many important structures in probability theory, information theory and statistics can be treated as structures in differential geometry by regarding a space of probabilities as a differential manifold endowed with a Riemannian metric and a family of affine connections.
		The Fisher information metric is a Riemannian 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.
	en.wikipedia.org /wiki/Information_geometry (878 words)

	B. Roy Frieden, Physics from Fisher Information
		Fisher information is a quantity devised by the great statistician R. Fisher in the 1920s, which is supposed to tell us how easy it is to learn about a probability distribution by sampling from it.
		Then the Fisher information, with respect to t, is the mean value of the square of the ratio between the derivative of p with respect to t and p itself --- I = <(dp(x;t)/dt 1/p(x;t))^2>, in the rather clunky symbols HTML allows.
		To get that, he subtracts from the Fisher information a new quantity of his own devising, the "bound information," and requires that the difference between these two, which he calls the "physical information," have stationary variation.
	www.cscs.umich.edu /~crshalizi/reviews/physics-from-fisher-info (2111 words)

	Amazon.com: Physics from Fisher Information: A Unification: Books: B. Roy Frieden (Site not responding. Last check: 2007-11-06)
		The information in question is, perhaps surprisingly, not Shannon or Boltzmann entropy but, rather, Fisher information, a simple concept little known to physicists.
		The information concept is applied 'phenomenally' to derive most known physics, from statistical mechanics and thermodynamics to quantum mechanics, the Einstein field equations, and quantum gravity.
		The information principle is based upon a new theory of measurement, one which incorporates the observer into the phenomenon that he/she observes.
	www.amazon.com /Physics-Fisher-Information-Roy-Frieden/dp/052163167X (2008 words)

	Fisher Matrix Confidence Bounds on the Parameters for the Weibull Distribution (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-11-06)
		Note that the variance and covariance of the parameters are obtained from the inverse Fisher information matrix as described in this section.
		The local Fisher information matrix is obtained from the second partials of the likelihood function, by substituting the solved parameter estimates into the particular functions.
		The Fisher matrix is one of the methodologies that Weibull++ uses for both MLE and regression analysis.
	www.weibull.com.cob-web.org:8888 /LifeDataWeb/fisher_matrix_confidence_bounds_on_the_parameters_for_the_weibull_distribution.htm (320 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		info.ordinal.cat -- Calculates the contribution to the fisher information matrix from an observation of icat.
		Routines which estimate the noncentrality parameter: lr.noncent -- Calculate the noncentrality parameter and degrees of freedom for the lr method using the fisher information matrix, alternative hypothesis parameters and constraint matrix.
		A is a matrix such that A*theta = (phi,lambda) where phi are the parameters constrained by the null hypothesis and lambda and the parameters which are not constrained.
	www.jstatsoft.org /v02/i02/dist/INDEX (1247 words)

	An Introduction to Markov Chain Monte Carlo
		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
		Thus, it follows directly from equation (9) that the information matrix is proportional to the identity and that the invariant measure is proportional to the Lebesgue measure on \bbbr
	omega.albany.edu:8008 /entpriors.html (5178 words)

	4.4 Fisher information
		A very important property of the ML estimators is that asymptotically (i.e., for a signal-to-noise ratio tending to infinity) they are (i) unbiased, and (ii) they have a Gaussian distribution with covariance matrix equal to the inverse of the Fisher information matrix.
		Because the projected Fisher matrix is the inverse of the intrinsic-parameter submatrix of the covariance matrix
		Because the trace of a matrix is equal to the sum of its eigenvalues, the matrix
	www.univie.ac.at /EMIS/journals/LRG/Articles/lrr-2005-3/articlesu8.html (439 words)

	The Information Matrix: Statistical Applications (Site not responding. Last check: 2007-11-06)
		The Fisher information matrix plays a central role in the practice and theory of statistical estimation.
		This matrix provides a summary of the amount of information in the data relative to the quantities of interest.
		Unfortunately, the analytical calculation of the information matrix is often a difficult or impossible task.
	www.science.gmu.edu /csi899.3/past/abstract/spall99.htm (139 words)

	NOTATION AND THEORY (Site not responding. Last check: 2007-11-06)
		Most computer programs print the diagonal and the upper or lower triangular of the variance-covariance matrix, which makes no difference since the matrix is symmetric.
		In (5) X is the design matrix, W is a diagonal matrix of inverse variance weights and Y is the column vector of residuals.
		where C is the contrast matrix forming the desired linear combination of the regression coefficients for the three-parameter test.
	www.jstatsoft.org /v02/i04/covar/node3.html (463 words)

	Are We Cruising a Hypothesis Space?
		This paper is about Information Geometry, a relatively new subject within mathematical statistics that attempts to study the problem of inference by using tools from modern differential geometry.
		On the other hand, physicists may see information geometry as a possible language for the elusive theory of quantum gravity since it is a language already made out of the right ingredients: uncertainty and differential geometry.
		I believe that one of the most promising areas for research in the field of information geometry is the clarification of the role of curvature in statistical inference.
	omega.albany.edu:8008 /cruise.html (2657 words)

	Systems Biology: Stochastic Dynamical Analysis of Gene Network
		Here we propose a sensitivity analysis methodology based on the Fisher information matrix, which is applied to a Circadian gene network.
		The FIM can be interpreted as a consolidation of sensitivities, which gives the basis of the proposed sensitivity measures.
		The optimal set of measurements are determined a priori using a geometric approach based on decomposition of the Fisher Information Matrix (FIM) into contributions from each measurement.
	www.engineering.ucsb.edu /~gunawan/research.html (615 words)

	Ill-conditioned problems, Fisher information and weak instruments
		The existence of a uniformly consistent estimator for a particular parameter is well-known to depend on the uniform continuity of the functional that defines the parameter in terms of the model.
		We show that der can be directly related to the familiar statistical concepts of Fisher information and identification, and also to the condition numbers that are used to measure ‘distance from an ill-posed problem’ in other branches of applied mathematics.
		We begin the analysis assuming a fully parametric setting, but then generalize to the nonparametric case, where the inverse of the Fisher information matrix is replaced by the covariance matrix of the efficient influence function.
	ideas.repec.org /p/ifs/cemmap/04-05.html (623 words)

	UCSB’s BioSens
		Though the FIM was originally used to represent the amount of information contained in a given set of signals/measurements about the model parameters, it also can be interpreted as a consolidation of the system sensitivities.
		The setup is the same as the FIM tool, but the settings are used to compute the only the diagonal of the Fisher Information Matrix (rather than the entire matrix).
		According to the Cramer-Rao theorem, the (inverse of) Fisher Information Matrix gives the lower bound for the variances in the parameter estimates from which the standard deviations can be computed.
	www.cs.ucsb.edu /~staylor/biosens/V2P1/BioSens_User_Guide.htm (4095 words)

	Abstract: Crame'r-Rao Bounds and Monte Carlo Calculation of the Fisher Information Matrix in Difficult Problems (Site not responding. Last check: 2007-11-06)
		The Fisher information matrix summarizes the amount of information in the data relative to the quantities of interest.
		There are many applications of the information matrix in modeling, systems analysis, and estimation, including confidence region calculation, input design, prediction bounds, and "noninformative" priors for Bayesian analysis.
		This paper reviews some basic principles associated with the information matrix, presents a resampling-based method for computing the information matrix together with some new theory related to efficient implementation, and presents some numerical results.
	www.galaxy.gmu.edu /Interface04/ABSTRACTS/abstract_03106.html (159 words)

	[No title]
		The IFIM is often the covariance matrix of the MLEs.
		But the larger the covariance matrix involved in Lk, the smaller the likelihood will be, and the larger will be -2 log likelihood.
		It involves the covariance matrix of the estimates, whereas the likelihood involves the covariance matrix of the residuals.) The factor a(n) is to be thought of as a per-parameter penalty.
	www.uic.edu /classes/idsc/ids594/research/MSCs/MSCs.doc (1139 words)

	Conference Materials
		We have discovered a new scheme to represent the Fisher information matrix of a stochastic multi-layer perceptron.
		Based on this scheme, we have designed an algorithm to compute the inverse of the Fisher information matrix.
		The inverse of the Fisher information matrix is used in the natural gradient descent algorithm to train single-layer or multi-layer perceptrons.
	cognet.mit.edu /library/conferences/paper?paper_id=2075 (124 words)

	What's the physics meaning for fisher information matrix?
		AIUI the Fisher information matrix for a parameter estimation problem is
		the Fisher Matrix (as in mathworld), reduce to estimating the covariance
		Apols, should have said the Fisher matrix is the inverse of the parameter
	sci4um.com /ntopic51.html (338 words)

	Amazon.com: Science from Fisher Information: A Unification: Books: B. Roy Frieden (Site not responding. Last check: 2007-11-06)
		This work shows 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 book greatly expands the material in Physics from Fisher Information to include many other areas in science.
	www.amazon.com /Science-Fisher-Information-Roy-Frieden/dp/0521009111 (1813 words)

	fisher - OneLook Dictionary Search
		Fisher, fisher : UltraLingua English Dictionary [home, info]
		Phrases that include fisher: bottom fisher, international fisher effect, fisher ideal index, fisher index, fisher information matrix, more...
		Words similar to fisher: fisherman, pekan, fl cat, fisher cat, martes pennanti, more...
	www.onelook.com /?w=fisher (283 words)

	Multivariate normal distribution - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-11-06)
		It is important to realize that the covariance matrix must be allowed to be singular.
		and the ML estimator of the covariance matrix is
		is the determinant of the covariance matrix Σ.
	en.wikipedia.org.cob-web.org:8888 /wiki/Multivariate_normal_distribution (1106 words)

	Confidence Bounds for the Lognormal Distribution (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-11-06)
		The method used by the application in estimating the different types of confidence bounds for lognormally distributed data is presented in this section.
		Note that there are closed-form solutions for both the normal and lognormal reliability that can be obtained without the use of the Fisher information matrix.
		To achieve consistent application across all possible data types, Weibull++ always uses the Fisher matrix in computing confidence intervals.
	www.weibull.com.cob-web.org:8888 /LifeDataWeb/confidence_bounds_log.htm (134 words)

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