Related papers: A Measurement-Based Robust Non-Gaussian Process Em…

Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

Weakly stationary Gaussian processes (GPs) are the principal tool in the statistical approaches to the design and analysis of computer experiments (or Uncertainty Quantification). Such processes are fitted to computer model output using a…

This paper proposes a novel purely measurement-based method for estimating dynamic load parameters in near real-time when stochastic load fluctuations are present. By leveraging on the regression theorem for the Ornstein-Uhlenbeck process,…

This paper studies worst-case robust optimal tracking using noisy input-output data. We utilize behavioral system theory to represent system trajectories, while avoiding explicit system identification. We assume that the recent output data…

The Power Law Process, also known as Non-Homogeneous Poisson Process, has been used in various aspects, one of which is the software reliability assessment. Specifically, by using its intensity function to compute the rate of change of a…

Semi-numerical models of reionization typically involve a large number of unknown parameters whose values are constrained by comparing with observations. Increasingly often, exploring this parameter space using semi-numerical simulations…

We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior…

We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may…

Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters…

Assuming an exponential power distribution is one way to deal with outliers in regression and clustering, which can increase the robustness of the analysis. Gaussian distribution is a special case of an exponential distribution. And an…

This work is about a slow-fast data assimilation system under non-Gaussian noisy fluctuations. Firstly, we show the existence of a random invariant manifold for a stochastic dynamical system with non-Gaussian noise and two-time scales.…

In dealing with high-dimensional data, factor models are often used for reducing dimensions and extracting relevant information. The spectrum of covariance matrices from power data exhibits two aspects: 1) bulk, which arises from random…

Electrical fault classification is vital for ensuring the reliability and safety of power systems. Accurate and efficient fault classification methods are essential for timely and effective maintenance. In this paper, we propose a novel…

We address the problem of estimating the uncertainty in the solution of power grid inverse problems within the framework of Bayesian inference. We investigate two approaches, an adjoint-based method and a stochastic spectral method. These…

This paper is concerned with robust performance criteria for linear continuous time invariant stochastic systems driven by statistically uncertain random processes. The uncertainty is understood as the deviation of imprecisely known…

With the continued deployment of synchronized Phasor Measurement Units (PMUs), high sample rate data are rapidly increasing the real time observability of power systems. Prior research has shown that the statistics of these data can provide…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

We consider the problem of reconstructing the dynamic state matrix of transmission power grids from time-stamped PMU measurements in the regime of ambient fluctuations. Using a maximum likelihood based approach, we construct a family of…

Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…