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A method providing optimal estimate of probability density functions (PDFs) from time series is proposed. It allows almost arbitrary resolution PDFs when applied to either, sampled analytic functions or digitized data from experiments. When…

A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…

Random processes play a crucial role in scientific research, often characterized by distribution functions or probability density functions (PDFs). These PDFs serve as essential approximations of the actual and frequently undisclosed…

Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…

Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few…

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…

If two probability density functions (PDFs) have values for their first $n$ moments which are quite close to each other (upper bounds of their differences are known), can it be expected that the PDFs themselves are very similar? Shown below…

We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…

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…

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…

The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis…

The likelihood calculation of a vast number of particles is the computational bottleneck for the particle filter in applications where the observation information is rich. For fast computing the likelihood of particles, a numerical fitting…

The class of location-scale finite mixtures is of enduring interest both from applied and theoretical perspectives of probability and statistics. We prove the following results: to an arbitrary degree of accuracy, (a) location-scale…

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…

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 normalized probability density function (PDF) of global measures of a large class of highly correlated systems has previously been demonstrated to fall on a single non-Gaussian "universal" curve. We derive the functional form of the…

This paper investigates probability density functions (PDFs) that are continuous everywhere, nearly uniform around the mode of distribution, and adaptable to a variety of distribution shapes ranging from bell-shaped to rectangular. From the…

Approximate Bayesian computation (ABC) methods, which are applicable when the likelihood is difficult or impossible to calculate, are an active topic of current research. Most current ABC algorithms directly approximate the posterior…

Reliable density estimation is fundamental for numerous applications in statistics and machine learning. In many practical scenarios, data are best modeled as mixtures of component densities that capture complex and multimodal patterns.…

We review various methods used to estimate uncertainties in quantum correlation functions, such as parton distribution functions (PDFs). Using a toy model of a PDF, we compare the uncertainty estimates yielded by the traditional Hessian and…