Related papers: Variational non-Bayesian inference of the Probabil…
Variational Bayesian inference is an important machine-learning tool that finds application from statistics to robotics. The goal is to find an approximate probability density function (PDF) from a chosen family that is in some sense…
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…
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This…
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the…
Bayesian estimation strategies represent the most fundamental formulation of the state estimation problem available, and apply readily to nonlinear systems with non-Gaussian uncertainties. The present paper introduces a novel method for…
Classical nonlinear dynamical systems are often characterized by their steady-state probability distribution functions (PDFs). Typically, PDFs are accumulated from numerical simulations that involve solving the underlying dynamical…
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…
Traditional Bayesian approaches for model uncertainty quantification rely on notoriously difficult processes of marginalization over each network parameter to estimate its probability density function (PDF). Our hypothesis is that internal…
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) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two…
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…
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the…
A robust uncertainty estimate in global analyses of Parton Distribution Functions (PDFs) is essential at the Large Hadron Collider (LHC), especially in view of the high-precision data anticipated by experimentalists in the High-Luminosity…
The probability density function (PDF) for critical wavefunction amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
We discuss a Bayesian methodology for the solution of the inverse problem underlying the determination of parton distribution functions (PDFs). In our approach, Gaussian Processes (GPs) are used to model the PDF prior, while Bayes theorem…
We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…
The probability density function (PDF) of some global average quantity plays a fundamental role in critical and highly correlated systems. We explicitly compute this quantity as a function of the magnetization for the two dimensional XY…
In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A set of parallel…
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…