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In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
This report presents an algorithm for determining the unknown rates in the sequential processes of a Stochastic Process Algebra model, provided that the rates in the combined flat model are given. Such a rate lifting is useful for model…
Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from…
Meaningful climate predictions must be accompanied by their corresponding range of uncertainty. Quantifying the uncertainties is non-trivial, and different methods have been suggested and used in the past. Here, we propose a method that…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…
This paper presents foundational theoretical results on distributed parameter estimation for undirected probabilistic graphical models. It introduces a general condition on composite likelihood decompositions of these models which…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
We present an identity for an unbiased estimate of a general statistical distribution. The identity computes the distribution density from dividing a histogram sum over a local window by a correction factor from a mean-force integral, and…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
The problem of computing functions of values at the nodes in a network in a totally distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer,…
Many existing approaches for estimating parameters in settings with distributional shifts operate under an invariance assumption. For example, under covariate shift, it is assumed that $p(y|x)$ remains invariant. We refer to such…
In this paper, using spectral theory of Hilbertian operators, we study ARMA Gaussian processes indexed by graphs. We extend Whittle maximum likelihood estimation of the parameters for the corresponding spectral density and show their…
Within the calibration of material models, often the numerical results of a simulation model $y$ are compared with the experimental measurements $y^*$. Usually, the differences between measurements and simulation are minimized using least…
We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
A multifidelity method for the nonlinear propagation of uncertainties in the presence of stochastic accelerations is presented. The proposed algorithm treats the uncertainty propagation (UP) problem by separating the propagation of the…
We consider Markov decision processes (MDPs) in which the transition probabilities and rewards belong to an uncertainty set parametrized by a collection of random variables. The probability distributions for these random parameters are…