Related papers: Dimensional reduction for sampled priors and appli…

A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution. The Bayesian estimator induced by a least favorable prior,…

We investigate the use of normalizing flow (NF) models as flexible priors in Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling for iterative Bayesian calibration. Trained on posteriors from previous analyses, these models can…

Varying coefficient models (VCMs) are widely used for estimating nonlinear regression functions for functional data. Their Bayesian variants using Gaussian process priors on the functional coefficients, however, have received limited…

Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve also as building blocks in more complex formulations, such as density regression, nonparametric…

We investigate how ideas from covariance localization in numerical weather prediction can be used in Markov chain Monte Carlo (MCMC) sampling of high-dimensional posterior distributions arising in Bayesian inverse problems. To localize an…

In this work we are interested in the (ill-posed) inverse problem for absolute permeability characterization that arises in predictive modeling of porous media flows. We consider a Bayesian statistical framework with a preconditioned Markov…

While Bayesian methods are extremely popular in statistics and machine learning, their application to massive datasets is often challenging, when possible at all. Indeed, the classical MCMC algorithms are prohibitively slow when both the…

We consider continuous-time diffusion models driven by fractional Brownian motion. Observations are assumed to possess a non-trivial likelihood given the latent path. Due to the non-Markovianity and high-dimensionality of the latent paths,…

Inverse problems lend themselves naturally to a Bayesian formulation, in which the quantity of interest is a posterior distribution of state and/or parameters given some uncertain observations. For the common case in which the forward…

Forthcoming Stage-IV dark energy optical surveys, such as LSST, have the ambitious goal of measuring cosmological parameters at sub-percent precision. Realizing their full scientific potential requires very precise measurement of the cosmic…

Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference…

Deconvolution of astronomical images is a key aspect of recovering the intrinsic properties of celestial objects, especially when considering ground-based observations. This paper explores the use of diffusion models (DMs) and the Diffusion…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

We present methods to rigorously extract parameter combinations that are constrained by data from posterior distributions. The standard approach uses linear methods that apply to Gaussian distributions. We show the limitations of the linear…

We consider the problem of Bayesian parameter estimation for deep neural networks, which is important in problem settings where we may have little data, and/ or where we need accurate posterior predictive densities, e.g., for applications…

Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We…

This work presents a model reduction approach to the inverse problem in the application of subsurface flows. For the Bayesian inverse problem, the forward model needs to be repeatedly computed for a large number of samples to get a…

A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…

We demonstrate a measure for the effective number of parameters constrained by a posterior distribution in the context of cosmology. In the same way that the mean of the Shannon information (i.e. the Kullback-Leibler divergence) provides a…

We propose a Bayesian image super-resolution (SR) method with a causal Gaussian Markov random field (MRF) prior. SR is a technique to estimate a spatially high-resolution image from given multiple low-resolution images. An MRF model with…