ABSTRACT A natural Bayesian approach for mixture models with an unknown number of
components is to take the usual finite mixture model with symmetric Dirichlet weights, and …

Penalized regression methods, such as L 1 regularization, are routinely used in high-
dimensional applications, and there is a rich literature on optimality properties under sparsity …

In this paper, I review the main results on the asymptotic properties of the posterior
distribution in nonparametric or high-dimensional models. In particular, I explain how …

We study convergence rates of variational posterior distributions for nonparametric and high-
dimensional inference. We formulate general conditions on prior, likelihood and variational …

Bayesian fractional posteriors Page 1 The Annals of Statistics 2019, Vol. 47, No. 1, 39–66
https://doi.org/10.1214/18-AOS1712 © Institute of Mathematical Statistics, 2019 BAYESIAN …

For data assumed to come from a finite mixture with an unknown number of components, it
has become common to use Dirichlet process mixtures (DPMs) not only for density …

We propose a Bayesian approach to regression with a scalar response on vector and tensor
covariates. Vectorization of the tensor prior to analysis fails to exploit the structure, often …

We show that rate-adaptive multivariate density estimation can be performed using
Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on …

In many applications, a finite mixture is a natural model, but it can be difficult to choose an
appropriate number of components. To circumvent this choice, investigators are increasingly …

Clustering is an important task in many areas of knowledge: medicine and epidemiology,
genomics, environmental science, economics, visual sciences, among others …