Related papers: Fisher Information of Scale
Fine-tuning and naturalness, the sensitivity of low-energy observables to small changes in the fundamental parameters of a theory, are cornerstones of physics beyond the Standard Model. We propose a new measure of fine-tuning based on…
Fisher's information measure plays a very important role in diverse areas of theoretical physics. The associated measures as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the…
We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…
Maximum likelihood estimates and corresponding confidence regions of the estimates are commonly used in statistical inference. In practice, people often construct approximate confidence regions with the Fisher information at given sample…
Information theory provides a useful tool to understand the evolution of complex nonlinear systems and their sustainability. In particular, Fisher Information (FI) has been evoked as a useful measure of sustainability and the variability of…
In the present paper, we would like to draw attention to a possible generalized Fisher information that fits well in the formalism of nonextensive thermostatistics. This generalized Fisher information is defined for densities on…
New inequalities are proved for the variance of the Pitman estimators (minimum variance equivariant estimators) of \theta constructed from samples of fixed size from populations F(x-\theta). The inequalities are closely related to the…
In this paper, we study an asymptotic approximation of the Fisher information for the estimation of a scalar parameter using quantized measurements. We show that, as the number of quantization intervals tends to infinity, the loss of Fisher…
We consider the problem of estimating an arbitrary dynamical parameter of an quantum open system in the input-output formalism. For irreducible Markov processes, we show that in the limit of large times the system-output state can be…
A relationship between the Fisher information and the characteristic function is established with the help of two inequalities. A necessary and sufficient condition for equality is found. These results are used to determine the asymptotic…
Structured optical beams possess rich spatial features that are commonly characterized using entropic measures of field complexity. However, such measures do not directly quantify the operational usefulness of optical structure for…
The basic properties of the Fisher information allow to reveal the statistical meaning of classical inequalities between mean functions. The properties applied to scale mixtures of Gaussian distributions lead to a new mean function of…
We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized $q$-Gaussian…
The Fisher information matrix (FIM) is a fundamental quantity to represent the characteristics of a stochastic model, including deep neural networks (DNNs). The present study reveals novel statistics of FIM that are universal among a wide…
Fisher Information is a key notion in the whole field of quantum metrology. It allows for a direct quantification of maximal achievable precision of estimation of parameters encoded in quantum states using the most general quantum…
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 employ a unified framework for computing the information capacity of biological signaling systems using Fisher Information. By deriving closed-form or easily computable information capacity formulas, we quantify how well different…
The quantum Fisher information represents the continuous family of metrics on the space of quantum states and places the fundamental limit on the accuracy of quantum state estimation. We show that the entire family of the quantum Fisher…
The convergence to stable laws is studied in relative Fisher information for sums of i.i.d. random variables.
Discrete events alter how parameter influence propagates in hybrid systems. Prevailing Fisher information formulations assume that sensitivities evolve smoothly according to continuous-time variational equations and therefore neglect the…