Related papers: Bayesian Estimation of Inverse Gaussian Distributi…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior…

A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…

In recent years, the shortcomings of Bayesian posteriors as inferential devices have received increased attention. A popular strategy for fixing them has been to instead target a Gibbs measure based on losses that connect a parameter of…

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…

In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian…

Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…

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…

This paper deals with the Bayesian estimation of high dimensional Gaussian graphical models. We develop a quasi-Bayesian implementation of the neighborhood selection method of Meinshausen and Buhlmann (2006) for the estimation of Gaussian…

Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…

One of the fundamental problems in Bayesian statistics is the approximation of the posterior distribution. Gibbs sampler and coordinate ascent variational inference are renownedly utilized approximation techniques that rely on stochastic…

The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…

For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…

Sampling from matrix generalized inverse Gaussian (MGIG) distributions is required in Markov Chain Monte Carlo (MCMC) algorithms for a variety of statistical models. However, an efficient sampling scheme for the MGIG distributions has not…

In Bayesian statistics, many problems can be expressed as the evaluation of the expectation of a quantity of interest with respect to the posterior distribution. Standard Monte Carlo method is often not applicable because the encountered…

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of…