Related papers: Indicator Functions: Distilling the Information fr…
We find that, even in the presence of discreteness noise, a Gaussianizing transform (producing a more-Gaussian one-point distribution) reduces nonlinearities in the power spectra of cosmological matter and galaxy density fields, in many…
We study the problem of estimating the magnitude of a Gaussian beam displacement using a two pixel or 'split' detector. We calculate the maximum likelihood estimator, and compute its asymptotic mean-squared-error via the Fisher information.…
Estimating the angular separation between two incoherently radiating monochromatic point sources is a canonical toy problem to quantify spatial resolution in imaging. In recent work, Tsang {\em et al.} showed, using a Fisher Information…
Skew-symmetric densities recently received much attention in the literature, giving rise to increasingly general families of univariate and multivariate skewed densities. Most of those families, however, suffer from the inferential drawback…
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 study the probability distribution $F(u)$ of the maximum of smooth Gaussian fields defined on compact subsets of $\R^d$ having some geometric regularity. Our main result is a general formula for the density of $F$. Even though this is an…
Marked power spectra provide a computationally efficient way to extract non-Gaussian information from the matter density field using the usual analysis tools developed for the power spectrum without the need for explicit calculation of…
We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…
We analyze the photometric redshift catalog of the Sloan Digital Sky Survey Data Release 5 (SDSS DR5) to estimate the Fisher information in the galaxy angular power spectrum with the help of the Rimes-Hamilton technique. It is found that…
Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by…
Information theory is an excellent framework for analyzing Earth system data because it allows us to characterize uncertainty and redundancy, and is universally interpretable. However, accurately estimating information content is…
Analytic continuation of imaginary time or frequency data to the real axis is a crucial step in extracting dynamical properties from quantum Monte Carlo simulations. The average spectrum method provides an elegant solution by integrating…
We here introduce indicator functions, which identify regions of a given density in order to characterize the density dependence of clustering. After a general introduction to this tool, we show that indicator-function power spectra are…
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…
Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…
The power spectrum of the nonlinearly evolved large-scale mass distribution recovers only a minority of the information available on the mass fluctuation amplitude. We investigate the recovery of this information in 2D "slabs" of the mass…
One way of recovering information about the initial conditions of the Universe is by measuring features of the cosmological density field which are preserved during gravitational evolution and galaxy formation. In this paper we study the…
Strong gravitational lensing gives access to the total mass distribution of galaxies. It can unveil a great deal of information about the lenses dark matter content when combined with the study of the lenses light profile. However,…
In modern contexts, some types of data are observed in high-resolution, essentially continuously in time. Such data units are best described as taking values in a space of functions. Subject units carrying the observations may have…
In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts…