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In this paper, we introduce new Stein identities for gamma target distribution as well as a new non-linear channel specifically designed for gamma inputs. From these two ingredients, we derive an explicit and simple formula for the…

Probability · Mathematics 2019-08-20 Benjamin Arras , Yvik Swan

The Bayesian decision-theoretic approach to design of experiments involves specifying a design (values of all controllable variables) to maximise the expected utility function (expectation with respect to the distribution of responses and…

Statistics Theory · Mathematics 2021-09-24 Antony M. Overstall

Markov Random Field models are powerful tools for the study of complex systems. However, little is known about how the interactions between the elements of such systems are encoded, especially from an information-theoretic perspective. In…

Information Theory · Computer Science 2015-03-19 Alexandre L. M. Levada

Using a representation of the score function by means of the divergence operator we exhibit a sufficient condition, in terms of the negative moments of the norm of the Malliavin derivative, under which convergence in Fisher information to…

Probability · Mathematics 2013-12-23 Ivan Nourdin , David Nualart

Skew-symmetric densities recently received much attention in the literature, giving rise to increasingly general families of univariate and multivariate skewed densities. Most of those families, however, suffer from the inferential drawback…

Statistics Theory · Mathematics 2012-07-03 Marc Hallin , Christophe Ley

Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical…

Statistics Theory · Mathematics 2023-06-05 Brodie A. J. Lawson , Kevin Burrage , Kerrie Mengersen , Rodrigo Weber dos Santos

The Fisher-Rao metric from Information Geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of Information Geometry to study more general phase transitions in…

Statistical Mechanics · Physics 2016-05-04 Omri Har Shemesh , Rick Quax , Alfons G. Hoekstra , Peter M. A. Sloot

In this paper, we analyze the impact of compressed sensing with complex random matrices on Fisher information and the Cram\'{e}r-Rao Bound (CRB) for estimating unknown parameters in the mean value function of a complex multivariate normal…

Statistics Theory · Mathematics 2023-07-19 Pooria Pakrooh , Ali Pezeshki , Louis L. Scharf , Douglas Cochran , Stephen D. Howard

Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed tolerance $\delta$. The lower bound is given on the basis of…

Quantum Physics · Physics 2018-01-10 Naoto Kura , Masahito Ueda

Many real-world tasks include some kind of parameter estimation, i.e., determination of a parameter encoded in a probability distribution. Often, such probability distributions arise from stochastic processes. For a stationary stochastic…

Quantum Physics · Physics 2023-06-08 Marco Radaelli , Gabriel T. Landi , Kavan Modi , Felix C. Binder

The dynamics of a charged two-qubit system prepared initially in a maximum entangled state is discussed, where each qubit interacts independently with a dephasing channel. The Fisher information is used to estimate the channel and the…

Quantum Physics · Physics 2016-12-13 Hamada El-Shiekh Nour Zidan , Nasser Metwally

We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional $J[g^{\mu\nu}(\theta^i)]$, where $g^{\mu\nu}(\theta^i)$ is the Fisher metric.…

Statistical Mechanics · Physics 2009-11-10 Xavier Calmet , Jacques Calmet

The Fisher information matrix provides a way to measure the amount of information given observed data based on parameters of interest. Many applications of the FIM exist in statistical modeling, system identification, and parameter…

Computation · Statistics 2021-04-16 Xuan Wu

We consider the problem of distributed estimation of a Gaussian vector with linear observation model. Each sensor makes a scalar noisy observation of the unknown vector, quantizes its observation, maps it to a digitally modulated symbol,…

Information Theory · Computer Science 2020-05-01 Mojtaba Shirazi , Azadeh Vosoughi

Recently proposed methods in data subset selection, that is active learning and active sampling, use Fisher information, Hessians, similarity matrices based on gradients, and gradient lengths to estimate how informative data is for a…

Machine Learning · Computer Science 2022-11-08 Andreas Kirsch , Yarin Gal

An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…

Probability · Mathematics 2012-05-01 S. G. Bobkov , G. P. Chistyakov , F. Götze

We propose the generalised Fisher information or the one-parameter extended class of the Fisher information for the case of one random variable. This new form of the Fisher information is obtained from the intriguing connection between the…

Statistics Theory · Mathematics 2022-08-25 Worachet Bukaew , Sikarin Yoo-Kong

This paper extends the idea of a generalized estimator for a scalar parameter (Vos, 2022) to multi-dimensional parameters both with and without nuisance parameters. The title reflects the fact that generalized estimators provide more than…

Statistics Theory · Mathematics 2024-08-26 Paul Vos , Qiang Wu

Lower bounds for the average probability of error of estimating a hidden variable X given an observation of a correlated random variable Y, and Fano's inequality in particular, play a central role in information theory. In this paper, we…

Information Theory · Computer Science 2013-10-08 Flavio du Pin Calmon , Mayank Varia , Muriel Médard , Mark M. Christiansen , Ken R. Duffy , Stefano Tessaro

Mutual information is a general statistical dependency measure which has found applications in representation learning, causality, domain generalization and computational biology. However, mutual information estimators are typically…

Machine Learning · Statistics 2023-10-17 Paweł Czyż , Frederic Grabowski , Julia E. Vogt , Niko Beerenwinkel , Alexander Marx