We have discussed stationary and dynamical properties of the information entropies in the Langevin model subjected to additive and multiplicative noise. Analytical expressions for the time-dependent Tsallis entropy and Fisher information have been obtained with the use of the dynamical moment approach to the FokkerPlanck equation, which was developed in a previous study [H. Hasegawa, Phys. Rev....

The Fisher matrix formalism has in recent times become the standard method for predicting the precision with which various cosmological parameters can be extracted from future data. This approach is fast, and generally returns accurate estimates for the parameter errors when the individual parameter likelihoods approximate a Gaussian distribution. However, where Gaussianity is not respected (du...

The capacity and the reliability function as the peak constraint tends to zero are considered for a discrete-time memoryless channel with peak constrained inputs. Prelov and van der Meulen showed that under mild conditions the ratio of the capacity to the squared peak constraint converges to one-half the maximum eigenvalue of the Fisher information matrix and if the Fisher information matrix is...

We investigate behavior of the Fisher information matrix of general stable distributions. Du-Mouchel (1975, 1983) proved that the Fisher information I αα of characteristic exponent α diverges to infinity as α approaches 2. Nagaev and Shkol'nik (1988) made more detailed analysis of I αα and derived asymptotic behavior of I αα diverging to infinity as α approaches 2 in the symmetric case. Extendi...

In this paper, we consider a parametric hidden Markov model where the hidden state space is non necessarily finite. We provide a necessary and sufficient condition for the invertibility of the limiting Fisher information matrix.

This note summarizes various derivations, formulas and computational algorithms relevant to the Fisher information matrix of Gaussian graphical models with respect to either an exponential parameterization (related to the information form) or the corresponding moment parameterization. 1 Gauss-Markov Models The probability density of a Gaussian random vector x ∈ R may be expressed in information...

The Fisher information matrix (FIM) is a critical quantity in several aspects of mathematical modeling, including input selection and confidence region calculation. Analytical determination of the FIM in a general setting, specially in nonlinear models, may be difficult or almost impossible due to intractable modeling requirements and/or intractable high-dimensional integration. To circumvent t...