Related papers: Approximate Reference Prior for Gaussian Random Fi…

This paper investigates the approximation of Gaussian random variables in Banach spaces, focusing on the high-probability bounds for the approximation of Gaussian random variables using finitely many observations. We derive non-asymptotic…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…

Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…

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…

In this paper we give a completely new approach to the problem of covariate selection in linear regression. A covariate or a set of covariates is included only if it is better in the sense of least squares than the same number of Gaussian…

A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…

Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces…

Gaussian distributions are widely used in Bayesian variational inference to approximate intractable posterior densities, but the ability to accommodate skewness can improve approximation accuracy significantly, when data or prior…

Bayesian methodologies prioritising accurate associations above sparsity in Gaussian graphical model (GGM) estimation remain relatively scarce in scientific literature. It is well accepted that the $\ell_2$ penalty enjoys a smaller…

We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…

Additive Bayesian networks are types of graphical models that extend the usual Bayesian generalized linear model to multiple dependent variables through the factorisation of the joint probability distribution of the underlying variables.…

The biased net paradigm was the first general and empirically tractable scheme for parameterizing complex patterns of dependence in networks, expressing deviations from uniform random graph structure in terms of latent ``bias events,''…

Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors.…

Probabilistic neural networks are typically modeled with independent weight priors, which do not capture weight correlations in the prior and do not provide a parsimonious interface to express properties in function space. A desirable class…

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…

In this paper we propose to numerically assess the performance of standard Gaussian approximations to probe the posterior distribution that arises from Bayesian data assimilation in petroleum reservoirs. In particular we assess the…

Learned priors based on deep generative models offer data-driven regularization for seismic inversion, but training them requires a dataset of representative subsurface models -- a resource that is inherently scarce in geoscience…

A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its…

The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power…

Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…