Related papers: An efficient approach to global sensitivity analys…
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…
The Simplified Modal Method (SMM) provides a quick and intuitive way to analyze the performance of gratings of rectangular shapes. For non-rectangular shapes, a version of SMM has been developed, but it applies only to the Littrow-mounting…
This paper is dedicated to method for spectral and polarization selective optical systems properties investigations for accurate analysis of nonclassical diffraction gratings properties: aspherical surfaces, variable grating step, variable…
We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…
We introduce a numerical method that enables efficient modelling of light scattering by large, disordered ensembles of non-spherical particles incorporated in stratified media, including when the particles are in close vicinity to each…
Metasurfaces enable powerful control of electromagnetic waves using subwavelength planar structures, but their deeply subwavelength periodicity typically suppresses propagating diffraction orders, which limits the number of available…
This article introduces two absolutely continuous global-local shrinkage priors to enable stochastic variable selection in the context of high-dimensional matrix exponential spatial specifications. Existing approaches as a means to dealing…
A new method for estimation of intragranular strain fields in polycrystalline materials based on scanning three-dimensional X-ray diffraction data (scanning-3DXRD) is presented and evaluated. Given an apriori known anisotropic compliance,…
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model which must be estimated. Although the…
The Van Allen radiation belts in the magnetosphere have been extensively studied using models based on radial diffusion theory, which is based on a quasi-linear approach with prescribed inner and outer boundary conditions. The 1-d diffusion…
We present a systematic accuracy assessment of the thin-element approximation (TEA), the beam propagation method (BPM), and the wave propagation method (WPM) for binary diffractive gratings, using the rigorous Fourier modal method (FMM) as…
In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…
Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their inference is very slow due to a need for many (e.g., 2000) iterations of sequential…
The diffraction contrast modalities accessible by X-ray grating interferometers are not imaged directly but have to be inferred from sine like signal variations occurring in a series of images acquired at varying relative positions of the…
Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This…
We develop a fast and scalable computational framework to solve large-scale and high-dimensional Bayesian optimal experimental design problems. In particular, we consider the problem of optimal observation sensor placement for Bayesian…
Electron backscatter diffraction is a powerful tool for mapping crystallographic microstructures. However, the primary crux to improving orientation accuracy and applying the technique to challenging materials lies in the correct…
This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…
The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…
The global sensitivity analysis of a complex numerical model often calls for the estimation of variance-based importance measures, named Sobol' indices. Metamodel-based techniques have been developed in order to replace the cpu…