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The accurate computation of the covariance matrix of fitted model parameters is a somewhat neglected task in Statistics. Algorithms are given for computing accurate covariance matrices derived from computing the Hessian matrix by numerical…

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…

This letter provides the first prediction of the probability density function (PDF) of flux $R$ in plasma sheath sheath region in magnetic fusion devices which is characterized by dynamical equations with exponential non-linearities. By…

This paper covers the material of our two talks. We describe a series of projects based upon perturbative expansions to follow the gravitational evolution of the one point probability distribution functions (PDFs) for the density contrast…

The need for accurate photometric redshifts estimation is a topic that has fundamental importance in Astronomy, due to the necessity of efficiently obtaining redshift information without the need of spectroscopic analysis. We propose a…

We critically assess the robustness of uncertainties on parton distribution functions (PDFs) determined using neural networks from global sets of experimental data collected from multiple experiments. We view the determination of PDFs as an…

Cosmic voids contain higher-order cosmological information and are of interest for astroparticle physics. Finding genuine matter underdensities in sparse galaxy surveys is, however, an underconstrained problem. Traditional void finding…

We use probability density functions (pdfs) of sums of orbit coordinates, over time intervals of the order of one Hubble time, to distinguish weakly from strongly chaotic orbits in a barred galaxy model. We find that, in the weakly chaotic…

Parton distribution functions (PDFs) form an essential part of particle physics calculations. Currently, the most precise predictions for these non-perturbative functions are generated through fits to global data. A problem that several PDF…

Cosmological surveys aim at answering fundamental questions about our Universe, including the nature of dark matter or the reason of unexpected accelerated expansion of the Universe. In order to answer these questions, two important…

Data analysis from upcoming large galaxy redshift surveys, such as Euclid and DESI will significantly improve constraints on cosmological parameters. To optimally extract the information from these galaxy surveys, it is important to control…

A probability density function (PDF) of a spatially dependent field provides a means of calculating moments of the field or, equivalently, the proportion of a spatial domain that is mapped to a given set of values. This paper describes a…

Under ideal conditions, the probability density function (PDF) of a random variable, such as a sensor measurement, would be well known and amenable to computation and communication tasks. However, this is often not the case, so the user…

Halo Occupation Distribution (HOD) models help us to connect observations and theory, by assigning galaxies to dark matter haloes. In this work we study one of the components of HOD models: the probability distribution function (PDF), which…

This paper outlines an approach to the approximation of probability density functions by quadratic forms of weighted orthonormal basis functions with positive semi-definite Hermitian matrices of unit trace. Such matrices are called…

We study gravitational lensing with a multiple lens plane approach, proposing a simple analytical model for the probability distribution function (PDF) of the dark matter convergence, kappa, for the different lens planes in a given…

To understand the nature of the accelerated expansion of the Universe, we need to combine constraints on the expansion rate and growth of structure. The growth rate is usually extracted from three dimensional galaxy maps by exploiting the…

A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically…

The probability density function (PDF) plays a central role in statistical and machine learning modeling. Real-world data often deviates from Gaussian assumptions, exhibiting skewness and exponential decay. To evaluate how well different…

Density estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in…