Related papers: Convergence Rates for Hierarchical Gibbs Samplers
In this paper, we describe centering and noncentering methodology as complementary techniques for use in parametrization of broad classes of hierarchical models, with a view to the construction of effective MCMC algorithms for exploring…
The level set approach has proven widely successful in the study of inverse problems for interfaces, since its systematic development in the 1990s. Recently it has been employed in the context of Bayesian inversion, allowing for the…
This work studies the convergence and finite sample approximations of entropic regularized Wasserstein distances in the Hilbert space setting. Our first main result is that for Gaussian measures on an infinite-dimensional Hilbert space,…
Importance weighted variational inference (Burda et al., 2015) uses multiple i.i.d. samples to have a tighter variational lower bound. We believe a joint proposal has the potential of reducing the number of redundant samples, and introduce…
Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…
In this paper, we establish the $R$-linear rate of convergence of a golden ratio algorithm for solving an equilibrium problem in a Hilbert space. Several experiments are performed to show the numerical behavior of the algorithm and also to…
In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables…
This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…
Gibbs sampling is a Markov Chain Monte Carlo (MCMC) method often used in Bayesian learning. MCMC methods can be difficult to deploy on parallel and distributed systems due to their inherently sequential nature. We study asynchronous Gibbs…
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years,…
We derive an upper bound for the efficiency of estimating entries in the inverse covariance matrix of a high dimensional distribution. We show that in order to approximate an off-diagonal entry of the density matrix of a $d$-dimensional…
The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…
This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…
Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…
Multivariate Bayesian error-in-variable (EIV) linear regression is considered to account for additional additive Gaussian error in the features and response. A 3-variable deterministic scan Gibbs samplers is constructed for multivariate EIV…
This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…
In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…
This paper devises a fully Bayesian sample size determination method for hierarchical model-based small area estimation with a decision risk approach. A new loss function specified around a desired maximum posterior variance target…
We consider the estimation of wealth inequality measures with their confidence interval, based on survey data with interval censoring. We rely on a Bayesian hierarchical model. It consists of a model where, due to survey sampling and unit…