Related papers: On optimal designs for non-regular models
We identify fundamental tradeoffs between statistical utility and privacy under local models of privacy in which data is kept private even from the statistician, providing instance-specific bounds for private estimation and learning…
A relationship between the Fisher information and the characteristic function is established with the help of two inequalities. A necessary and sufficient condition for equality is found. These results are used to determine the asymptotic…
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…
The selection of optimal designs for generalized linear mixed models is complicated by the fact that the Fisher information matrix, on which most optimality criteria depend, is computationally expensive to evaluate. Our focus is on the…
Bayesian optimal experiments that maximize the information gained from collected data are critical to efficiently identify behavioral models. We extend a seminal method for designing Bayesian optimal experiments by introducing two…
We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive…
The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can…
This paper studies semiparametric Fisher information in models parametrized by general normed spaces. The main contribution is to establish that positive semiparametric Fisher information is equivalent to the gradient of the parameter of…
In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different…
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…
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…
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…
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…
We introduce a positive Hermitian operator, the Fisher operator, and use it to examine a measurement process incorporating unitary dynamics and complete measurements. We develop the idea of information complement, the minimization of which…
Fisher's Method of Maximum Likelihood is shown to be a procedure for the construction of likelihood intervals or regions, instead of a procedure of point estimation. Based on Fisher's articles and books it is justified that by estimation…
Fisher (1934) argued that certain ancillary statistics form a relevant subset, a subset of the sample space on which inference should be restricted, and showed that conditioning on their observed value reduces the dimension of the data…
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…
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…
Current experimental design techniques for dynamical systems often only incorporate measurement noise, while dynamical systems also involve process noise. To construct experimental designs we need to quantify their information content. The…
Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which…