Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust
linear regression. Combining the likelihood of a multivariate robust linear regression model …

We establish asymptotic normality of the batch means estimator of MCMC variance for
reversible geometrically ergodic chains. Existing results use assumptions which are not …

Tremendous progress has been made in the last two decades in the area of high-
dimensional regression, especially in the “large p, small n” setting. Such sample starved …

The utility of a Markov chain Monte Carlo algorithm is, in large part, determined by the size of
the spectral gap of the corresponding Markov operator. However, calculating (and even …

Consistent estimation of the spectrum of trace class Data Augmentation algorithms Page 1
Bernoulli 25(4B), 2019, 3832–3863 https://doi.org/10.3150/19-BEJ1112 Consistent estimation of …

When Gaussian errors are inappropriate in a multivariate linear regression setting, it is often
assumed that the errors are iid from a distribution that is a scale mixture of multivariate …

This dissertation focuses on two fundamental areas in Markov chain Monte Carlo (MCMC)
research: uncertainty assessment and asymptotic properties for Monte Carlo estimators, and …

The Horseshoe is a widely used and popular continuous shrinkage prior for high-
dimensional Bayesian linear regression. Recently, regularized versions of the Horseshoe …