Related papers: Non-parametric estimation of Fisher information fr…
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…
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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,…
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…