Related papers: Convergence Rates for Bayesian Estimation and Test…
This work is concerned with nonparametric goodness-of-fit testing in the context of nonlinear inverse problems with random observations. Bayesian posterior distributions based upon a Gaussian process prior distribution are proven to…
In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…
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…
Constrained learning is prevalent in many statistical tasks. Recent work proposes distance-to-set penalties to derive estimators under general constraints that can be specified as sets, but focuses on obtaining point estimates that do not…
Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
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…
In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…
We consider the nonparametric multivariate isotonic regression problem, where the regression function is assumed to be nondecreasing with respect to each predictor. Our goal is to construct a Bayesian credible interval for the function…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
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…
We study the posterior contraction rates of a Bayesian method with Gaussian process priors in nonparametric regression and its plug-in property for differential operators. For a general class of kernels, we establish convergence rates of…
Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of…
In Bayesian decision theory, it is known that robustness with respect to the loss and the prior can be improved by adding new observations. In this article we study the rate of robustness improvement with respect to the number of…
In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…
We study frequentist properties of a Bayesian high-dimensional multivariate linear regression model with correlated responses. The predictors are separated into many groups and the group structure is pre-determined. Two features of the…
We investigate the problem of deriving posterior concentration rates under different loss functions in nonparametric Bayes. We first provide a lower bound on posterior coverages of shrinking neighbourhoods that relates the metric or loss…
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…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…
In the Bayes paradigm and for a given loss function, we propose the construction of a new type of posterior distributions, that extends the classical Bayes one, for estimating the law of an $n$-sample. The loss functions we have in mind are…