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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

As we enter the era of quantum technologies, quantum estimation theory provides an operationally motivating framework for determining high precision devices in modern technological applications. The aim of any estimation process is to…

Quantum Physics · Physics 2022-05-02 Abdallah Slaoui , Lalla Btissam Drissi , El Hassan Saidi , Rachid Ahl Laamara

The expected decrease in system inertia and frequency stability motivates the development and maintenance of dynamic system models by Transmission System Operators. However, some dynamic model parameters can be unavailable due to market…

Signal Processing · Electrical Eng. & Systems 2025-05-27 Dawn Virginillo , Asja Derviškadić , Mario Paolone

We show that the mathematical form of the information measure of Fisher's I for a Gibbs' canonical probability distribution (the most important one in statistical mechanics) incorporates important features of the intrinsic structure of…

Statistical Mechanics · Physics 2007-05-23 F. Pennini , A. Plastino

An approach based on the Fisher information (FI) is developed to quantify the maximum information gain and optimal experimental design in neutron reflectometry experiments. In these experiments, the FI can be analytically calculated and…

Data Analysis, Statistics and Probability · Physics 2021-08-03 James H. Durant , Lucas Wilkins , Keith Butler , Joshaniel F. K. Cooper

Quantum Fisher information matrix (QFIM) is a cornerstone of modern quantum metrology and quantum information geometry. Apart from optimal estimation, it finds applications in description of quantum speed limits, quantum criticality,…

Quantum Physics · Physics 2018-04-16 Dominik Šafránek

A deep neural network is a hierarchical nonlinear model transforming input signals to output signals. Its input-output relation is considered to be stochastic, being described for a given input by a parameterized conditional probability…

Machine Learning · Computer Science 2018-08-23 Shun-ichi Amari , Ryo Karakida , Masafumi Oizumi

This paper deals with the problem of estimating the coupling constant $\theta$ of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal…

Quantum Physics · Physics 2011-06-23 Madalin Guta

Pairwise comparison models have been widely used for utility evaluation and rank aggregation across various fields. The increasing scale of modern problems underscores the need to understand statistical inference in these models when the…

Statistics Theory · Mathematics 2025-12-16 Ruijian Han , Wenlu Tang , Yiming Xu

The quality of numerical reconstructions for unknown parameters in inverse problems depends fundamentally on the selection of experimental data. To ensure a robust reconstruction, it is crucial to select data that are sensitive to the…

Numerical Analysis · Mathematics 2026-04-14 Kathrin Hellmuth , Christian Klingenberg , Qin Li

The concept of Fisher information can be useful even in cases where the probability distributions of interest are not absolutely continuous with respect to the natural reference measure on the underlying space. Practical examples where this…

Statistics Theory · Mathematics 2018-03-28 Jeremie Houssineau , Ajay Jasra , Sumeetpal S. Singh

We consider the impact that temporal correlations in the measurement statistics can have on the achievable precision in a sequential metrological protocol. In this setting, and for a single quantum probe, we establish that it is the…

Quantum Physics · Physics 2024-04-02 Eoin O'Connor , Steve Campbell , Gabriel T. Landi

Mimicking the maximum likelihood estimator, we construct first order Cramer-Rao efficient and explicitly computable estimators for the scale parameter $\sigma^2$ in the model $Z_{i,n}=\sigma n^{-\beta}X_i+Y_i,i=1,\ldots,n,\beta>0$ with…

Statistics Theory · Mathematics 2015-03-20 Till Sabel , Johannes Schmidt-Hieber

Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…

Machine Learning · Statistics 2014-01-24 Keisuke Yamazaki

The optimal phase estimation strategy is derived when partial a priori knowledge on the estimated phase is available. The structure of the optimal measurements, estimators and the optimal probe states is analyzed. The results fill the gap…

Quantum Physics · Physics 2013-05-29 Rafal Demkowicz-Dobrzanski

In biology, information flows from the environment to the genome by the process of natural selection. But it has not been clear precisely what sort of information metric properly describes natural selection. Here, I show that Fisher…

Populations and Evolution · Quantitative Biology 2009-06-18 Steven A. Frank

We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be…

Quantum Physics · Physics 2017-08-02 Yu Chen , Haidong Yuan

Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the…

Quantum Physics · Physics 2014-12-30 Tzu-Chao Hung

Spectroscopy detected in the time domain entails many techniques, such as FTIR, pump-probe, FT-Raman, and 2DES, and applications, such as molecule characterization, excited state dynamics studies, or spectra classifications. Surprisingly,…

Optics · Physics 2024-05-21 Luca Bolzonello , Niek F van Hulst , Andreas Jakobsson

Classically, Fisher information is the relevant object in defining optimal experimental designs. However, for models that lack certain regularity, the Fisher information does not exist and, hence, there is no notion of design optimality…

Statistics Theory · Mathematics 2019-12-04 Yi Lin , Ryan Martin , Min Yang