Related papers: Effects of correlated variability on information e…
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…
We examine how the informational properties of a confined single ion response in a Paul trap modified by optical-lattice. We focus on the ground and first excited motional states and show that Fisher information, Shannon entropy, and…
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…
This study explores the interaction between non-extensive entropic FLRW cosmology and the power-law inflationary model, with a focus on the overlap between the scalar spectral index `$n_s$' and the tensor-to-scalar ratio `$r$'. Based on a…
Complex frequency excitations, oscillating signals whose amplitude decreases exponentially in time, have recently been demonstrated to significantly increase the effective quality factor of mechanical resonators. In this work, we…
Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…
Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PD's) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in…
Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related…
We quantify the Fisher information content of the cosmic shear survey two-point function as a function of noise and resolution. The two point information of dark matter saturates at the trans-linear scale. We investigate the impact of…
We show that different entropic measures of fluctuations lead to contradictory uncertainty relations for two complementary observables. We apply Tsallis and R\'{e}nyi entropies to the joint distribution emerging from a noisy simultaneous…
We have discussed the validity of the factorization approximation (FA) and nonextensivity-induced correlation, by using the multivariate $q$-Gaussian probability distribution function (PDF) for $N$-unit independent nonextensive systems. The…
We investigate the connection between the time-evolution of averages of stochastic quantities and the Fisher information and its induced statistical length. As a consequence of the Cramer-Rao bound, we find that the rate of change of the…
The Fisher information matrix summarizes the amount of information in a set of data relative to the quantities of interest. There are many applications of the information matrix in statistical modeling, system identification and parameter…
This paper proposes a unifying variational approach for proving and extending some fundamental information theoretic inequalities. Fundamental information theory results such as maximization of differential entropy, minimization of Fisher…
A chain rule and a subadditivity for the entropy of type $\beta$, which is one of the nonadditive entropies, were derived by Z.Dar\'oczy. In this paper, we study the further relations among Tsallis type entropies which are typical…
We study a dynamical system with time dependent Hamiltonian by numerical experiments so as to find a relation between thermodynamics and chaotic nature of the system. Excess information loss, defined newly based on Lyapunov analysis, is…
In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large…
Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann- Gibbs form of the entropy ensures that…
The weak lensing power spectrum carries cosmological information via its dependence on the growth of structure and on geometric factors. Since much of the cosmological information comes from scales affected by nonlinear clustering,…
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…