Related papers: Dirichlet-Laplace priors for optimal shrinkage

Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While…

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…

We develop a general class of Bayesian repulsive Gaussian mixture models that encourage well-separated clusters, aiming at reducing potentially redundant components produced by independent priors for locations (such as the Dirichlet…

In many regression settings the unknown coefficients may have some known structure, for instance they may be ordered in space or correspond to a vectorized matrix or tensor. At the same time, the unknown coefficients may be sparse, with…

In recent years, shrinkage priors have received much attention in high-dimensional data analysis from a Bayesian perspective. Compared with widely used spike-and-slab priors, shrinkage priors have better computational efficiency. But the…

We introduce a new class of distributions named log-adjusted shrinkage priors for the analysis of sparse signals, which extends the three parameter beta priors by multiplying an additional log-term to their densities. The proposed prior has…

We study frequentist properties of Bayesian and $L_0$ model selection, with a focus on (potentially non-linear) high-dimensional regression. We propose a construction to study how posterior probabilities and normalized $L_0$ criteria…

Spatially inhomogeneous functions, which may be smooth in some regions and rough in other regions, are modelled naturally in a Bayesian manner using so-called Besov priors which are given by random wavelet expansions with…

In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity. In…

This work addresses the problem of high-dimensional classification by exploring the generalized Bayesian logistic regression method under a sparsity-inducing prior distribution. The method involves utilizing a fractional power of the…

Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…

We study the rate of convergence of posterior distributions in density estimation problems for log-densities in periodic Sobolev classes characterized by a smoothness parameter p. The posterior expected density provides a nonparametric…

This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and…

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…

Use of continuous shrinkage priors -- with a "spike" near zero and heavy-tails towards infinity -- is an increasingly popular approach to induce sparsity in parameter estimates. When the parameters are only weakly identified by the…

In a Bayesian context, prior specification for inference on monotone densities is conceptually straightforward, but proving posterior convergence theorems is complicated by the fact that desirable prior concentration properties often are…

We discuss a Bayesian hierarchical copula model for clusters of financial time series. A similar approach has been developed in recent paper. However, the prior distributions proposed there do not always provide a proper posterior. In order…

In a Bayesian inverse problem setting, the solution consists of a posterior measure obtained by combining prior belief, information about the forward operator, and noisy observational data. This measure is most often given in terms of a…

In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG…