Related papers: Edge-promoting adaptive Bayesian experimental desi…

Bayesian optimal experimental design is a sub-field of statistics focused on developing methods to make efficient use of experimental resources. Any potential design is evaluated in terms of a utility function, such as the (theoretically…

X-ray tomography has applications in various industrial fields such as sawmill industry, oil and gas industry, chemical engineering, and geotechnical engineering. In this article, we study Bayesian methods for the X-ray tomography…

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…

We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…

This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…

We investigate adaptive design based on a single sparse pilot scan for generating effective scanning strategies for computed tomography reconstruction. We propose a novel approach using the linearised deep image prior. It allows…

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…

Numerical integration and emulation are fundamental topics across scientific fields. We propose novel adaptive quadrature schemes based on an active learning procedure. We consider an interpolative approach for building a surrogate…

In recent investigations, the problem of detecting edges given non-uniform Fourier data was reformulated as a sparse signal recovery problem with an l1-regularized least squares cost function. This result can also be derived by employing a…

We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…

We consider optimal sensor placement for hyper-parameterized linear Bayesian inverse problems, where the hyper-parameter characterizes nonlinear flexibilities in the forward model, and is considered for a range of possible values. This…

We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…

A Bayesian approach to variable selection which is based on the expected Kullback-Leibler divergence between the full model and its projection onto a submodel has recently been suggested in the literature. Here we extend this idea by…

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…

We present an efficient method for computing A-optimal experimental designs for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we address the problem of optimizing the…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…