Related papers: Beyond Fisher Forecasting for Cosmology
We present a numerically cheap approximation to super-sample covariance (SSC) of large scale structure cosmological probes, first in the case of angular power spectra. It necessitates no new elements besides those used for the prediction of…
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…
(abridged) We study the validity of the approximation of a Gaussian cosmic shear likelihood. We estimate the true likelihood for a fiducial cosmological model from a large set of ray-tracing simulations and investigate the impact of…
In various fields of physics and astronomy, access to experimental facilities or to telescopes is becoming more and more competitive and limited. It becomes therefore important to optimize the type of measurements and their scheduling to…
The subjects of the paper are the likelihood method (LM) and the expected Fisher information (FI) considered from the point od view of the construction of the physical models which originate in the statistical description of phenomena. The…
This paper presents state estimation and stochastic optimal control gathered in one global optimization problem generating dual effect i.e. the control can improve the future estimation. As the optimal policy is impossible to compute, a…
Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In…
We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…
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 diagonal of a model's Fisher Information Matrix (the "Fisher diagonal") has frequently been used as a way to measure parameter sensitivity. Typically, the Fisher diagonal is estimated via squared sampled gradients of the model's…
We propose a modification of a maximum likelihood procedure for tuning parameter values in models, based upon the comparison of their output to field data. Our methodology, which uses polynomial approximations of the sample space to…
Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…
Natural Gradient Descent, a second-degree optimization method motivated by the information geometry, makes use of the Fisher Information Matrix instead of the Hessian which is typically used. However, in many cases, the Fisher Information…
Starting from the Fisher matrix for counts in cells, I derive the full Fisher matrix for surveys of multiple tracers of large-scale structure. The key assumption is that the inverse of the covariance of the galaxy counts is given by the…
Super-sample covariance (SSC) is an important effect for cosmological analyses that use the deep structure of the cosmic web; it may, however, be nontrivial to include it practically in a pipeline. We solve this difficulty by presenting a…
The likelihood-informed subspace (LIS) method offers a viable route to reducing the dimensionality of high-dimensional probability distributions arising in Bayesian inference. LIS identifies an intrinsic low-dimensional linear subspace…
For latent class models where the class weights depend on individual covariates, we derive a simple expression for computing the score vector and a convenient hybrid between the observed and the expected information matrices which is always…
In order to reach the required performance of Stage-III and IV weak lensing surveys, cosmic shear measurements have to rely on external simulations to calibrate residual biases. Over the years, several techniques have been developed to…
Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the…
An important mathematical tool in the analysis of dynamical systems is the approximation of the reach set, i.e., the set of states reachable after a given time from a given initial state. This set is difficult to compute for complex systems…