Related papers: A multiscale strategy for Bayesian inference using…

We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…

We present a Bayesian approach to identify optimal transformations that map model input points to low dimensional latent variables. The "projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to…

The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…

We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…

We propose a fully Bayesian approach for causal inference with multivariate categorical data based on staged tree models, a class of probabilistic graphical models capable of representing asymmetric and context-specific dependencies. To…

We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…

Data for several applications in diverse fields can be represented as multiple matrices that are linked across rows or columns. This is particularly common in molecular biomedical research, in which multiple molecular "omics" technologies…

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…

This paper proposes an effective treatment of hyperparameters in the Bayesian inference of a scalar field from indirect observations. Obtaining the joint posterior distribution of the field and its hyperparameters is challenging. The…

In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…

Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…

In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…

This work deals with an inverse two-dimensional nonlinear heat conduction problem to determine the top and lateral surface transfer coefficients. For this, the \textsc{B}ayesian framework with the \textsc{M}arkov Chain \textsc{M}onte…

Bayesian inference provides a rigorous methodology for estimation and uncertainty quantification of parameters in geophysical forward models. Badlands (basin and landscape dynamics model) is a landscape evolution model that simulates…

Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion…

The need to reason about uncertainty in large, complex, and multi-modal datasets has become increasingly common across modern scientific environments. The ability to transform samples from one distribution $P$ to another distribution $Q$…

Markov chain Monte Carlo (MCMC) sampling of posterior distributions arising in Bayesian inverse problems is challenging when evaluations of the forward model are computationally expensive. Replacing the forward model with a low-cost,…

In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational models can not resolve all scales. Various subgrid models are…

Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC)…