Related papers: Formal Definitions of Conservative Probability Dis…
Context. Whenever correlation functions are used for inference about cosmological parameters in the context of a Bayesian analysis, the likelihood function of correlation functions needs to be known. Usually, it is approximated as a…
Stretched exponential probability density functions (pdf), having the form of the exponential of minus a fractional power of the argument, are commonly found in turbulence and other areas. They can arise because of an underlying random…
This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density…
(Abridged) We discuss the probability distribution function (PDF) of column density resulting from density fields with lognormal PDFs, applicable to isothermal gas (e.g., probably molecular clouds). We suggest that a ``decorrelation…
The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre…
In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be…
Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…
Time series of observables measured from complex systems do often exhibit non-normal statistics, their statistical distributions (PDF's) are not gaussian and often skewed, with roughly exponential tails. Departure from gaussianity is…
The estimation of probability density functions (PDF) using approximate maps is a fundamental building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of a…
The properties of the probability distribution function of the cosmological continuous density field are studied. We present further developments and compare dynamically motivated methods to derive the PDF. One of them is based on the…
The evolution of probability distribution functions (PDFs) of continuous density, velocity and velocity derivatives ( deformation tensor) fields in the theory of cosmological gravitational instability are considered. We show that in the…
In this paper, we study the statistical evolution of the large-scale structure (LSS), focusing on the joint probability distribution function (PDF) of the coarse-grained cosmic field and its role in constructing effective dynamics. As the…
Density destructors are differentiable and invertible transforms that map multivariate PDFs of arbitrary structure (low entropy) into non-structured PDFs (maximum entropy). Multivariate Gaussianization and multivariate equalization are…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
We continue to explore the hypothesis that neuronal populations represent and process analog variables in terms of probability density functions (PDFs). A neural assembly encoding the joint probability density over relevant analog variables…
Two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions (PDFs). As the parameter is varied, one interpolates between the eigenvalue PDF for the superposition of two…
We study density fluctuations in supersonic turbulence using both theoretical methods and numerical simulations. A theoretical formulation is developed for the probability distribution function (PDF) of the density at steady state,…
Probability density functions (PDFs) can be understood as continuous compositions by the theory of Bayes spaces. The origin of a Bayes space is determined by a given reference measure. This can be easily changed through the well-known chain…
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…
Turbulence is essential for understanding the structure and dynamics of molecular clouds and star-forming regions. There is a need for adequate tools to describe and characterize the properties of turbulent flows. One-point probability…