Related papers: Likelihood method and Fisher information in constr…
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…
The Fisher information matrix (FIM) is a key quantity in statistics as it is required for example for evaluating asymptotic precisions of parameter estimates, for computing test statistics or asymptotic distributions in statistical testing,…
We study the classical and quantum Fisher information for the Lieb-Liniger model. The Fisher information has been studied extensively when the parameter is inscribed on a quantum state by a unitary process, e.g., Mach-Zehnder or Ramsey…
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…
The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either…
The unknown amplitude law q(x) defining an observed effect may be found using the principle of Extreme Physical Information. EPI is derived as follows. The observations follow an information flow J --> I, with J the information intrinsic to…
Many statistical models require an estimation of unknown (co)-variance parameter(s) in a model. The estimation usually obtained by maximizing a log-likelihood which involves log determinant terms. In principle, one requires the…
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…
This paper presents some results on the maximum likelihood (ML) estimation from incomplete data. Finite sample properties of conditional observed information matrices are established. They possess positive definiteness and the same Loewner…
Recently proposed methods in data subset selection, that is active learning and active sampling, use Fisher information, Hessians, similarity matrices based on gradients, and gradient lengths to estimate how informative data is for a…
In this paper, a new three-parameter lifetime distribution is introduced and many of its standard properties are discussed. These include shape of the probability density function, hazard rate function and its shape, quantile function,…
Quantum Fisher information (QFI) plays a vital role in quantum precision measurement, quantum information, many-body physics, and other domains. Obtaining the QFI from experiment for a quantum state reveals insights such as the limits of…
An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…
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…
The Fisher information matrix (FM) plays an important role in forecasts and inferences in many areas of physics. While giving fast parameter estimation with the Gaussian likelihood approximation in the parameter space, the FM can only give…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
In the recent years, information theory of quantum-mechanical systems have aroused the interest of many Theoretical Physicist. This due to the fact that it provides a deeper insight into the internal structure of the systems. Also, It is…
Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that…
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…
In the realm of deep learning, the Fisher information matrix (FIM) gives novel insights and useful tools to characterize the loss landscape, perform second-order optimization, and build geometric learning theories. The exact FIM is either…