相关论文: Hyper-differential sensitivity analysis in the con…

Joint modeling of spatially-oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…

High dimensional data has introduced challenges that are difficult to address when attempting to implement classical approaches of statistical process control. This has made it a topic of interest for research due in recent years. However,…

Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…

In many applications, Bayesian inverse problems can give rise to probability distributions which contain complexities due to the Hessian varying greatly across parameter space. This complexity often manifests itself as lower dimensional…

In this paper, we will consider an $hp$-finite elements discretization of a highly indefinite Helmholtz problem by some dG formulation which is based on the ultra-weak variational formulation by Cessenat and Depr\'{e}s. We will introduce an…

Diffuse optical tomography (DOT) is a severely ill-posed nonlinear inverse problem that seeks to estimate optical parameters from boundary measurements. In the Bayesian framework, the ill-posedness is diminished by incorporating {\em a…

Stochastic differential equations (SDEs) are increasingly used in longitudinal data analysis, compartmental models, growth modelling, and other applications in a number of disciplines. Parameter estimation, however, currently requires…

The majority of research on efficient and scalable algorithms in computational science and engineering has focused on the forward problem: given parameter inputs, solve the governing equations to determine output quantities of interest. In…

Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…

Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity…

A successful model for high-dimensional spatial extremes should, in principle, be able to describe both weakening extremal dependence at increasing levels and changes in the type of extremal dependence class as a function of the distance…

We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…

This paper considers a discrete-valued signal estimation scheme based on a low-complexity Bayesian optimal message passing algorithm (MPA) for solving massive linear inverse problems under highly correlated measurements. Gaussian belief…

While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…

In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…

Bayesian inverse problem on an infinite dimensional separable Hilbert space with the whole state observed is well posed when the prior state distribution is a Gaussian probability measure and the data error covariance is a cylindric…

This study investigates the variational posterior convergence rates of inverse problems for partial differential equations (PDEs) with parameters in Besov spaces $B_{pp}^\alpha$ ($p \geq 1$) which are modeled naturally in a Bayesian manner…

Inverse problems exist in many disciplines of science and engineering. In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems. Recently, denoising diffusion…