Related papers: Shape-Constrained Univariate Density Estimation
A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear…
Signal processing techniques will lean on blind methods in the near future, where no redundant, resource allocating information will be transmitted through the channel. To achieve a proper decision, however, it is essential to know at least…
We examine the state of statistical equilibrium attained by a uniformly forced condensable substance subjected to advection in a periodic domain. In particular, we examine the probability density function (\pdf{}) of the condensable…
We study a non-parametric approach to multivariate density estimation. The estimators are piecewise constant density functions supported by binary partitions. The partition of the sample space is learned by maximizing the likelihood of the…
Fusing probabilistic information is a fundamental task in signal and data processing with relevance to many fields of technology and science. In this work, we investigate the fusion of multiple probability density functions (pdfs) of a…
We introduce a method for calculating the probability density function (PDF) of a turbulent density field in three dimensions using only information contained in the projected two-dimensional column density field. We test the method by…
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 solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…
The effect of uncertainties and noise on a quantity of interest (model output) is often better described by its probability density function (PDF) than by its moments. Although density estimation is a common task, the adequacy of…
Volumetry is one of the principal downstream applications of 3D medical image segmentation, for example, to detect abnormal tissue growth or for surgery planning. Conformal Prediction is a promising framework for uncertainty quantification,…
In probability density function (PDF) methods a transport equation is solved numerically to compute the time and space dependent probability distribution of several flow variables in a turbulent flow. The joint PDF of the velocity…
Recent works have demonstrated that the convergence rate of a nonparametric density estimator can be greatly improved by using a low-rank estimator when the target density is a convex combination of separable probability densities with…
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way…
Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the…
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…
A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of…
Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for…
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).…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
We consider the distribution of the sum and the maximum of a collection of independent exponentially distributed random variables. The focus is laid on the explicit form of the density functions (pdf) of non-i.i.d. sequences. Those are…