Related papers: How to estimate Fisher information matrices from s…
Expected Fisher information can be found a priori and as a result its inverse is the primary variance approximation used in the design of experiments. This is in contrast to the common claim that the inverse of observed Fisher information…
In mixed linear models with nonnormal data, the Gaussian Fisher information matrix is called a quasi-information matrix (QUIM). The QUIM plays an important role in evaluating the asymptotic covariance matrix of the estimators of the model…
The Fisher matrix approach (Fisher 1935) allows one to calculate in advance how well a given experiment will be able to estimate model parameters, and has been an invaluable tool in experimental design. In the same spirit, we present here a…
The Fisher matrix (FM) has been generally used to predict the accuracy of the gravitational wave parameter estimation. Although a limitation of the FM has been well known, it is still mainly used due to its very low computational cost…
Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian…
The mean of an unknown variance-$\sigma^2$ distribution $f$ can be estimated from $n$ samples with variance $\frac{\sigma^2}{n}$ and nearly corresponding subgaussian rate. When $f$ is known up to translation, this can be improved…
A deep neural network is a hierarchical nonlinear model transforming input signals to output signals. Its input-output relation is considered to be stochastic, being described for a given input by a parameterized conditional probability…
The problem of preserving the privacy of individual entries of a database when responding to linear or nonlinear queries with constrained additive noise is considered. For privacy protection, the response to the query is systematically…
Recently there is a rising interest in the research of mean field optimization, in particular because of its role in analyzing the training of neural networks. In this paper by adding the Fisher Information as the regularizer, we relate the…
We prove that two well-known measures of information are interrelated in interesting and useful ways when applied to nonequilibrium circumstances. A nontrivial form of the lower bound for the Fisher information measure is derived in…
Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte…
Consider the centered Gaussian vector $X$ in $\R^n$ with covariance matrix $ \Sigma.$ Randomize $\Sigma$ such that $ \Sigma^{-1}$ has a Wishart distribution with shape parameter $p>(n-1)/2$ and mean $p\sigma.$ We compute the density…
This paper extends the idea of a generalized estimator for a scalar parameter (Vos, 2022) to multi-dimensional parameters both with and without nuisance parameters. The title reflects the fact that generalized estimators provide more than…
The conventional formulation of quantum sensing is based on the assumption that the probe is reset to its initial state after each measurement. In a very distinct approach, one can also pursue a sequential measurement scheme in which…
In this brief note we compute the Fisher information of a family of generalized normal distributions. Fisher information is usually defined for regular distributions, i.e. continuously differentiable (log) density functions whose support…
Quantum generalizations of the Fisher information are important in quantum information science, with applications in high energy and condensed matter physics and in quantum estimation theory, machine learning, and optimization. One can…
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…
Classically, Fisher information is the relevant object in defining optimal experimental designs. However, for models that lack certain regularity, the Fisher information does not exist and, hence, there is no notion of design optimality…
The Fisher information matrix of the cosmic microwave background (CMB) radiation power spectrum coefficients is a fundamental quantity that specifies the information content of a CMB experiment. In the most general case, its exact…
The estimation of continuous parameters from measured data plays a central role in many fields of physics. A key tool in understanding and improving such estimation processes is the concept of Fisher information, which quantifies how…