83 citations · 316 across the 25 of their papers we have counts for
26 papers
Extensions of the solidarity principle of the spectral gap for Gibbs samplers to their blocked and collapsed variants
Xavier Mak, James P. Hobert
Connections of a spectral nature are formed between Gibbs samplers and their blocked and collapsed variants. The solidarity principle of the spectral gap for full Gibbs samplers is…
The data augmentation algorithm
Vivekananda Roy, Kshitij Khare, James P. Hobert
The data augmentation (DA) algorithms are popular Markov chain Monte Carlo (MCMC) algorithms often used for sampling from intractable probability distributions. This review article…
On the convergence rate of the "out-of-order" block Gibbs sampler
Zhumengmeng Jin, James P. Hobert
It is shown that a seemingly harmless reordering of the steps in a block Gibbs sampler can actually invalidate the algorithm. In particular, the Markov chain that is simulated by t…
Approximating the Spectral Gap of the Pólya-Gamma Gibbs Sampler
Bryant Davis, James P. Hobert
The self-adjoint, positive Markov operator defined by the Pólya-Gamma Gibbs sampler (under a proper normal prior) is shown to be trace-class, which implies that all non-zero elemen…
Dimension free convergence rates for Gibbs samplers for Bayesian linear mixed models
Zhumengmeng Jin, James P. Hobert
The emergence of big data has led to a growing interest in so-called convergence complexity analysis, which is the study of how the convergence rate of a Monte Carlo Markov chain (…
On the convergence complexity of Gibbs samplers for a family of simple Bayesian random effects models
Bryant Davis, James P. Hobert
The emergence of big data has led to so-called convergence complexity analysis, which is the study of how Markov chain Monte Carlo (MCMC) algorithms behave as the sample size, ,…