Related papers: Ultra High-dimensional Multivariate Posterior Cont…

We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…

Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…

Selecting a subset of variables for linear models remains an active area of research. This paper reviews many of the recent contributions to the Bayesian model selection and shrinkage prior literature. A posterior variable selection summary…

We consider a family of infinite dimensional product measures with tails between Gaussian and exponential, which we call $p$-exponential measures. We study their measure-theoretic properties and in particular their concentration. Our…

There has been increased research interest in the subfield of sparse Bayesian factor analysis with shrinkage priors, which achieve additional sparsity beyond the natural parsimonity of factor models. In this spirit, we estimate the number…

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…

Bayesian sparse factor models have proven useful for characterizing dependence in multivariate data, but scaling computation to large numbers of samples and dimensions is problematic. We propose expandable factor analysis for scalable…

Local clock models propose that the rate of molecular evolution is constant within phylogenetic sub-trees. Current local clock inference procedures scale poorly to large taxa problems, impose model misspecification, or require a priori…

Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…

High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…

In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex…

Estimating a covariance matrix is an important task in applications where the number of variables is larger than the number of observations. Shrinkage approaches for estimating a high-dimensional covariance matrix are often employed to…

In the setting of nonparametric multivariate regression with unknown error variance, we study asymptotic properties of a Bayesian method for estimating a regression function f and its mixed partial derivatives. We use a random series of…

For ordinary matrix models, the eigenvalue probability density decays rapidly as one goes to infinity, in other words, has "short tails". This ensures that all the multiple trace correlators (multipoint moments) are convergent and…

In this paper, we analyze posterior consistency of a Bayesian data assimilation problem under discretization. We prove convergence rates for the discrete posterior to ground truth solution under both conforming discretization and finite…

Due to their flexibility and theoretical tractability Gaussian process (GP) regression models have become a central topic in modern statistics and machine learning. While the true posterior in these models is given explicitly, numerical…

General Bayesian updating replaces the likelihood with a loss scaled by a learning rate, but posterior uncertainty can depend sharply on that scale. We propose a simple post-processing that aligns generalized posterior draws with their…

Recently, high-dimensional heterogeneous data have attracted a lot of attention and discussion. Under heterogeneity, semiparametric regression is a popular choice to model data in statistics. In this paper, we take advantages of expectile…

Consider the problem of high dimensional variable selection for the Gaussian linear model when the unknown error variance is also of interest. In this paper, we show that the use of conjugate shrinkage priors for Bayesian variable selection…

Variable selection in the linear regression model takes many apparent faces from both frequentist and Bayesian standpoints. In this paper we introduce a variable selection method referred to as a rescaled spike and slab model. We study the…