Related papers: Generalised Fisher Matrices
Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters - both their errors and covariances. In this short review, I outline a…
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…
The planning and design of future experiments rely heavily on forecasting to assess the potential scientific value provided by a hypothetical set of measurements. The Fisher information matrix, due to its convenient properties and low…
The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and…
The Fisher information matrix is a quantity of fundamental importance for information geometry and asymptotic statistics. In practice, it is widely used to quickly estimate the expected information available in a data set and guide…
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…
The Fisher information matrix can be used to characterize the local geometry of the parameter space of neural networks. It elucidates insightful theories and useful tools to understand and optimize neural networks. Given its high…
For linear mixed models with co-variance matrices which are not linearly dependent on variance component parameters, we prove that the average of the observed information and the Fisher information can be split into two parts. The essential…
We consider the processing of statistical samples $X\sim P_\theta$ by a channel $p(y|x)$, and characterize how the statistical information from the samples for estimating the parameter $\theta\in\mathbb{R}^d$ can scale with the mutual…
A common approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating…
Theoretical studies in gravitational wave astronomy often require the calculation of Fisher Information Matrices and Likelihood functions, which in a direct approach entail the costly step of computing gravitational waveforms. Here I…
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…
Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise…
In this paper we extent the previously published DALI-approximation for likelihoods to cases in which the parameter dependency is in the covariance matrix. The approximation recovers non-Gaussian likelihoods, and reduces to the Fisher…
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…
We propose a modified $\chi^{\beta}$-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cram\'er-Rao inequalities, involving this Fisher information,…
The quantum Fisher information matrix is a central object in multiparameter quantum estimation theory. It is usually challenging to obtain analytical expressions for it because most calculation methods rely on the diagonalization of the…
In this brief paper we revisit the Fisher information content of cosmological power spectra or two-point functions of Gaussian fields in order to comment on the assumption of Gaussian estimators and the use of parameter-dependent covariance…
We derive a Fisher matrix for the parameters characterising a population of gravitational-wave events. This provides a guide to the precision with which population parameters can be estimated with multiple observations, which becomes…
Random Fisher matrices arise naturally in multivariate statistical analysis and understanding the properties of its eigenvalues is of primary importance for many hypothesis testing problems like testing the equality between two multivariate…