相关论文: The Inverse Gamma-Gamma Prior for Optimal Posterio…

In various applications, we deal with high-dimensional positive-valued data that often exhibits sparsity. This paper develops a new class of continuous global-local shrinkage priors tailored to analyzing gamma-distributed observations where…

Scale-mixture shrinkage priors have recently been shown to possess robust empirical performance and excellent theoretical properties such as model selection consistency and (near) minimax posterior contraction rates. In this paper, the…

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…

Heavy-tailed continuous shrinkage priors, such as the horseshoe prior, are widely used for sparse estimation problems. However, there is limited work extending these priors to predictors with grouping structures. Of particular interest in…

Suppose we have data generated according to a multivariate normal distribution with a fixed unknown mean vector that is sparse in the sense of being nearly black. Optimality of Bayes estimates and posterior concentration properties in terms…

The first Bayesian results for the sparse normal means problem were proven for spike-and-slab priors. However, these priors are less convenient from a computational point of view. In the meanwhile, a large number of continuous shrinkage…

We consider a high-dimensional sparse normal means model where the goal is to estimate the mean vector assuming the proportion of non-zero means is unknown. We model the mean vector by a one-group global-local shrinkage prior belonging to 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…

We introduce a strategy for specifying informative inverse-gamma (IG) priors for variance components in Bayesian multilevel models (MLMs), derived via transformations from chi-square to gamma to inverse-gamma distributions. A Monte Carlo…

We consider a class of non-conjugate priors as a mixing family of distributions for a parameter (e.g., Poisson or gamma rate, inverse scale or precision of an inverse-gamma, inverse variance of a normal distribution) of an exponential…

In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data.…

We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…

We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…

An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…

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…

When performing Bayesian data analysis using a general linear mixed model, the resulting posterior density is almost always analytically intractable. However, if proper conditionally conjugate priors are used, there is a simple two-block…

During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,…

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 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…

The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a MAP estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse…