Related papers: Indicator Functions: Distilling the Information fr…

The Fisher Information matrix is a widely used measure for applications ranging from statistical inference, information geometry, experiment design, to the study of criticality in biological systems. Yet there is no commonly accepted…

A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…

This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of…

Context. Weak lensing and clustering statistics beyond two-point functions can capture non-Gaussian information about the matter density field, thereby improving the constraints on cosmological parameters relative to the mainstream methods…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

Using large deviations results that characterize the amount of information per node on a two-dimensional (2-D) lattice, asymptotic behavior of a sensor network deployed over a correlated random field for statistical inference is…

Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we…

The maximum achievable rate or mutual informa- tion of multidimensional rotationally invariant distributions in the presence of additive white Gaussian noise is analyzed. A simple expression for the special case of multisphere distributions…

Most compressed sensing algorithms do not account for the effect of saturation in noisy compressed measurements, though saturation is an important consequence of the limited dynamic range of existing sensors. The few algorithms that handle…

We quantify the Fisher information content of the cosmic shear survey two-point function as a function of noise and resolution. The two point information of dark matter saturates at the trans-linear scale. We investigate the impact of…

How much visual information about the retinal images can be extracted from the different layers of the visual pathway?. Separate subsystems (e.g. opponent channels, spatial filters, nonlinearities of the texture sensors) have been suggested…

Low redshift surveys of galaxy peculiar velocities provide a wealth of cosmological information. We revisit the idea of extracting this information by directly measuring the redshift-space momentum power spectrum from such surveys. We…

Weak lensing maps contain information beyond two-point statistics on small scales. Much recent work has tried to extract this information through a range of different observables or via nonlinear transformations of the lensing field. Here…

In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…

Given a decision process based on the approximate probability density function returned by a data assimilation algorithm, an interaction level between the decision making level and the data assimilation level is designed to incorporate the…

Using a discrete wavelet based space-scale decomposition (SSD), the spectrum of the skewness and kurtosis is developed to describe the non-Gaussian signatures in cosmologically interesting samples. Because the basis of the discrete wavelet…

In active learning, acquisition functions define informativeness directly on the representation position within the model manifold. However, for most machine learning models (in particular neural networks) this representation is not fixed…

We explore scaling relations for the information carried by individual events, and how that information accumulates in catalogs like those from ground-based gravitational-wave detectors. For a variety of situations, the larger number of…

Here we characterized an information measure for cell polarity that applies to non-motile cells responding to a chemical gradient. The central idea is that polarization represents information about the direction of the gradient. We applied…

Gaussianizing transformations are used statistically in many non-cosmological fields, but in cosmology, we are only starting to apply them. Here I explain a strategy of analyzing the 1-point function (PDF) of a spatial field, together with…