Related papers: The split Gibbs sampler revisited: improvements to…
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…
We are concerned with a novel Bayesian statistical framework for the characterization of natural subsurface formations, a very challenging task. Because of the large dimension of the stochastic space of the prior distribution in the…
Many Bayesian inference problems involve target distributions whose density functions are computationally expensive to evaluate. Replacing the target density with a local approximation based on a small number of carefully chosen density…
In this chapter, we address the challenge of exploring the posterior distributions of Bayesian inverse problems with computationally intensive forward models. We consider various multivariate proposal distributions, and compare them with…
In geostatistics, Gaussian random fields are often used to model heterogeneities of soil or subsurface parameters. To give spatial approximations of these random fields, they are discretized. Then, different techniques of geostatistical…
Bayesian feature allocation models are a popular tool for modelling data with a combinatorial latent structure. Exact inference in these models is generally intractable and so practitioners typically apply Markov Chain Monte Carlo (MCMC)…
The problem of Bayesian reduced rank regression is considered in this paper. We propose, for the first time, to use Langevin Monte Carlo method in this problem. A spectral scaled Student prior distrbution is used to exploit the underlying…
The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient…
Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…
We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior…
This paper focuses on a challenging class of inverse problems that is often encountered in applications. The forward model is a complex non-linear black-box, potentially non-injective, whose outputs cover multiple decades in amplitude.…
Spatial whole-brain Bayesian modeling of task-related functional magnetic resonance imaging (fMRI) is a great computational challenge. Most of the currently proposed methods therefore do inference in subregions of the brain separately or do…
For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an…
Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such…
Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…
Bayesian Neural Networks(BNNs) with high-dimensional parameters pose a challenge for posterior inference due to the multi-modality of the posterior distributions. Stochastic Gradient MCMC(SGMCMC) with cyclical learning rate scheduling is a…
Markov Chain Monte Carlo (MCMC) methods have a drawback when working with a target distribution or likelihood function that is computationally expensive to evaluate, specially when working with big data. This paper focuses on…
This paper concerns the Bayesian approach to inverse acoustic scattering problems of inferring the position and shape of a sound-soft obstacle from phaseless far-field data generated by point source waves. To improve the convergence rate,…
An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where…
Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice,…