Related papers: From robust tests to Bayes-like posterior distribu…
We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite…
We investigate the asymptotic normality of the posterior distribution in the discrete setting, when model dimension increases with sample size. We consider a probability mass function $\theta_0$ on $\mathbbm{N}\setminus \{0\}$ and a…
We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…
Classic Bayesian methods with complex models are frequently infeasible due to an intractable likelihood. Simulation-based inference methods, such as Approximate Bayesian Computing (ABC), calculate posteriors without accessing a likelihood…
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…
Prior sensitivity analysis is a fundamental method to check the effects of prior distributions on the posterior distribution in Bayesian inference. Exploring the posteriors under several alternative priors can be computationally intensive,…
This paper investigates the {\em nonasymptotic} properties of Bayes procedures for estimating an unknown distribution from $n$ i.i.d.\ observations. We assume that the prior is supported by a model $(\scr{S},h)$ (where $h$ denotes the…
Posterior contractions rates (PCRs) strengthen the notion of Bayesian consistency, quantifying the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of the true model, with probability tending to 1 or…
Robust regression has attracted a great amount of attention in the literature recently, particularly for taking asymmetricity into account simultaneously and for high-dimensional analysis. However, the majority of research on the topics…
Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…
We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing…
Despite the popularism of Bayesian neural networks in recent years, its use is somewhat limited in complex and big data situations due to the computational cost associated with full posterior evaluations. Variational Bayes (VB) provides a…
We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…
The practical implementation of Bayesian inference requires numerical approximation when closed-form expressions are not available. What types of accuracy (convergence) of the numerical approximations guarantee robustness and what types do…
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…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
This paper investigates the consistency of a posterior distribution in the single-measurement fractional Calder\'on problem with additive Gaussian noise. We consider a Bayesian framework with rescaled and Gaussian sieve priors, using a…
We propose a simple robust hypothesis test that has the same sample complexity as that of the optimal Neyman-Pearson test up to constants, but robust to distribution perturbations under Hellinger distance. We discuss the applicability of…
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…
In a given problem, the Bayesian statistical paradigm requires the specification of a prior distribution that quantifies relevant information about the unknowns of main interest external to the data. In cases where little such information…