Related papers: Display of probability densities for data from a c…
Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain…
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…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
In this paper, based on a known formula, we use a simple idea to get a new representation for the density of Malliavin differentiable random variables. This new representation is particularly useful for finding lower bounds for the density.
A theoretical analysis of the statistical distributions of the reflected intensities from random media is presented. We use random matrix theory to analytically deduce the probability densities in the localization regime. Numerical…
We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed…
We examine the problem of computing the highest density region (HDR) in a computational context where the user has access to a density function and quantile function for the distribution (e.g., in the statistical language R). We examine…
We obtain sufficient conditions for the uniqueness of a probability solution to the stationary Kolmogorov equation with a degenerate diffusion matrix. We employ the method of doubling variables known in stochastic analysis directly to the…
Taylor dispersion analysis is an increasingly popular characterization method that measures the diffusion coefficient, and hence the hydrodynamic radius, of (bio)polymers, nanoparticles or even small molecules. In this work, we describe an…
The density ratio of two probability distributions is one of the fundamental tools in mathematical and computational statistics and machine learning, and it has a variety of known applications. Therefore, density ratio estimation from…
A density matrix $\rho$ may be represented in many different ways as a mixture of pure states, $\rho = \sum_i p_i |\psi_i\ra \la \psi_i|$. This paper characterizes the class of probability distributions $(p_i)$ that may appear in such a…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
We study a relaxation of the problem of coupling probability distributions -- a list of samples is generated from one distribution and an accept is declared if any one of these samples is identical to the sample generated from the other…
We prove results concerning the representation of a given distribution by means of a given random quantity. The existence of a solution to this problem is related to the notion of conglomerability, originally introduced by Dubins to study…
In this paper we discuss a simple method of testing for the presence of energy-dependent dispersion in high energy data-sets. It uses the minimisation of the Kolmogorov distance between the cumulative distribution of two probability…
Modeling large dependent datasets in modern time series analysis is a crucial research area. One effective approach to handle such datasets is to transform the observations into density functions and apply statistical methods for further…
Perhaps surprisingly, recent studies have shown probabilistic model likelihoods have poor specificity for out-of-distribution (OOD) detection and often assign higher likelihoods to OOD data than in-distribution data. To ameliorate this…
In this work we present an alternative method to obtain a distribution of particles over an hyper surface, such that they obey a rest-mass density distribution $\rho(x^i)$. We use density profiles that can be written as…
Let $\left(\Omega,\Sigma,p\right)$ be a probability measure space and let $X:\Omega\to{\mathbb{R}}^k$ be a (vector valued) random variable. We suppose that the probability $p_X$ induced by $X$ is absolutely continuous with respect to the…