Related papers: Multilevel higher order Quasi-Monte Carlo Bayesian…

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and…

In this paper, we propose a new stochastic optimization algorithm for Bayesian inference based on multilevel Monte Carlo (MLMC) methods. In Bayesian statistics, biased estimators of the model evidence have been often used as stochastic…

Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…

Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…

Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…

Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in Bayesian computations. However, they need to access the full data set in order to evaluate the posterior density at every step of the algorithm. This results in a great…

We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…

Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…

This work describes a domain embedding technique between two non-matching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is…

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…

In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Most scientific domains elicit the development of efficient algorithms and accessible scientific software. This thesis unifies our developments in three broad domains: Quasi-Monte Carlo (QMC) methods for efficient high-dimensional…

The Bayesian inversion method demonstrates significant potential for solving inverse problems, enabling both point estimation and uncertainty quantification (UQ). However, Bayesian maximum a posteriori (MAP) estimation may become unstable…

The efficient simulation of the mean value of a non-linear functional of the solution to a linear stochastic partial differential equation (SPDE) with additive Gaussian noise is considered. A Galerkin finite element method is employed along…

In this paper we propose an efficient stochastic optimization algorithm to search for Bayesian experimental designs such that the expected information gain is maximized. The gradient of the expected information gain with respect to…

In this article we consider a Bayesian inverse problem associated to elliptic partial differential equations (PDEs) in two and three dimensions. This class of inverse problems is important in applications such as hydrology, but the…

Sequential Monte Carlo (SMC) methods offer a principled approach to Bayesian uncertainty quantification but are traditionally limited by the need for full-batch gradient evaluations. We introduce a scalable variant by incorporating…

We propose a multilevel Monte Carlo-FEM algorithm to solve elliptic Bayesian inverse problems with "Besov random tree prior". These priors are given by a wavelet series with stochastic coefficients, and certain terms in the expansion…

In this paper we introduce a new multilevel Monte Carlo (MLMC) estimator for multi-dimensional SDEs driven by Brownian motions. Giles has previously shown that if we combine a numerical approximation with strong order of convergence…