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This paper studies a novel approach for approximating the behavior of compartmental spreading processes. In contrast to prior work, the methods developed describe a dynamics which bound the exact moment dynamics, without explicitly…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
Systematically simulating specular light transport requires an exhaustive search for primitive tuples containing admissible paths. Given the extreme inefficiency of enumerating all combinations, we propose to significantly reduce the search…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
In this paper we present a data-driven approach for uncertainty propagation. In particular, we consider stochastic differential equations with parametric uncertainty. Solution of the differential equation is approximated using maximum…
Maximum likelihood estimators are proposed for the parameters and the densities in a semiparametric density ratio model in which the nonparametric baseline density is approximated by the Bernstein polynomial model. The EM algorithm is used…
In many time-dependent problems of practical interest the parameters entering the equations describing the evolution of the various quantities exhibit uncertainty. One way to address the problem of how this uncertainty impacts the solution…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…
The Fourier-Bessel expansion of a function on a circular disc yields a simple series representation for the end-to-end probability distribution function w(R,phi) encountered in a planar persistent random walk, where the direction taken in a…
This paper presents a comprehensive study of nonparametric estimation techniques on the circle using Fej\'er polynomials, which are analogues of Bernstein polynomials for periodic functions. Building upon Fej\'er's uniform approximation…
In this work we develop a scalable computational framework for the solution of PDE-constrained optimal control under high-dimensional uncertainty. Specifically, we consider a mean-variance formulation of the control objective and employ a…
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…
Decisions about health interventions are often made using limited evidence. Mathematical models used to inform such decisions often include uncertainty analysis to account for the effect of uncertainty in the current evidence base on…
The recently introduced basis adaptation method for Homogeneous (Wiener) Chaos expansions is explored in a new context where the rotation/projection matrices are computed by discovering the active subspace where the random input exhibits…
Motivated by a theorem of Barbour, we revisit some of the classical limit theorems in probability from the viewpoint of the Stein method. We setup the framework to bound Wasserstein distances between some distributions on infinite…
We present a method to automatically approximate moment-based invariants of probabilistic programs with non-polynomial updates of continuous state variables to accommodate more complex dynamics. Our approach leverages polynomial chaos…
As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling…
We present and examine a result related to uncertainty reasoning, namely that a certain plausibility space of Cox's type can be uniquely embedded in a minimal ordered field. This, although a purely mathematical result, can be claimed to…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…