Related papers: A Short Research Note on Calculating Exact Distrib…
Statistical studies of astronomical data sets, in particular of cataloged properties for discrete objects, are central to astrophysics. One cannot model those objects' population properties or incidences without a quantitative understanding…
We show how an adequate post--Newtonian generalization can be obtained for Newtonian dark matter halos associated with an empiric density profile. Applying this approach to halos that follow from the well known numerical simulations of…
Learning the multivariate distribution of data is a core challenge in statistics and machine learning. Traditional methods aim for the probability density function (PDF) and are limited by the curse of dimensionality. Modern neural methods…
We present a new algorithm for efficiently computing the $N$-point correlation functions (NPCFs) of a 3D density field for arbitrary $N$. This can be applied both to a discrete spectroscopic galaxy survey and a continuous field. By…
A new and simple statistical approach is performed to calculate the parton distribution functions (PDFs) of the nucleon in terms of light-front kinematic variables. We do not put in any extra arbitrary parameter or corrected term by hand,…
Modern analysis on parton distribution functions (PDFs) requires calculations of the log-likelihood functions from thousands of experimental data points, and scans of multi-dimensional parameter space with tens of degrees of freedom. In…
We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…
We introduce an analytic surface density profile for dark matter halos that accurately reproduces the structure of simulated halos of mass $M_{\rm vir} = 10^{7-11}\ M_\odot$, making it useful for modeling line-of-sight perturbers in strong…
Simulation-based inference methods that feature correct conditional coverage of confidence sets based on observations that have been compressed to a scalar test statistic require accurate modeling of either the p-value function or the…
We present a novel way of using neural networks (NN) to estimate the redshift distribution of a galaxy sample. We are able to obtain a probability density function (PDF) for each galaxy using a classification neural network. The method is…
We present marginal cumulative distribution functions (CDF) for density matrices $\rho$ of fixed purity $\tfrac{1}{N}\le\mu_N(\rho)=\textrm{Tr}[\rho^2]\le 1$ for arbitrary dimension $N$. We give closed form analytic formulas for the cases…
We test different implementations of the halo occupation distribution (HOD) model to reconstruct the spatial distribution of galaxies as predicted by a publicly available semi-analytical model (SAM). We compare the measured two-point…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
In this paper we demonstrate that multi-modal Probability Distribution Functions (PDFs) may be efficiently sampled using an algorithm originally developed for numerical integrations by Monte-Carlo methods. This algorithm can be used to…
We construct a set of parton distribution functions (PDFs) in which fixed-order NLO and NNLO calculations are supplemented with soft-gluon (threshold) resummation up to NLL and NNLL accuracy respectively, suitable for use in conjunction…
The output distribution of a neural network (NN) over the entire input space captures the complete input-output mapping relationship, offering insights toward a more comprehensive NN understanding. Exhaustive enumeration or traditional…
N-body simulations predict that dark matter halos with different mass scales are described by a universal model, the Navarro-Frenk-White (NFW) density profiles. As a consequence of baryonic cooling effects, the halos will become more…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
The analysis of gravitational lensing by galaxies and galaxy clusters typically relies on ellipsoidal lens models to describe the deflection of light by the involved dark-matter halos. These models are most often based on the isothermal…
The selection of a specific statistical distribution is seldom a simple problem. One strategy consists in testing different distributions (normal, lognormal, Weibull, etc.), and selecting the one providing the best fit to the observed data…