3.1k citations · 3.8k across the 32 of their papers we have counts for
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Explicit Constraints on the Geometric Rate of Convergence of Random Walk Metropolis-Hastings
Riddhiman Bhattacharya, Galin L. Jones
Convergence rate analyses of random walk Metropolis-Hastings Markov chains on general state spaces have largely focused on establishing sufficient conditions for geometric ergodici…
Convergence Analysis of Data Augmentation Algorithms for Bayesian Robust Multivariate Linear Regression with Incomplete Data
Haoxiang Li, Qian Qin, Galin L. Jones
Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust linear regression. Combining the likelihood of a multivariate robust linear regression m…
Lower bounds on the rate of convergence for accept-reject-based Markov chains in Wasserstein and total variation distances
Austin Brown, Galin L. Jones
To avoid poor empirical performance in Metropolis-Hastings and other accept-reject-based algorithms practitioners often tune them by trial and error. Lower bounds on the convergenc…
Exact Convergence Analysis for Metropolis-Hastings Independence Samplers in Wasserstein Distances
Austin Brown, Galin L. Jones
Under mild assumptions, we show the exact convergence rate in total variation is also exact in weaker Wasserstein distances for the Metropolis-Hastings independence sampler. We dev…
Convergence Rates of Two-Component MCMC Samplers
Qian Qin, Galin L. Jones
Component-wise MCMC algorithms, including Gibbs and conditional Metropolis-Hastings samplers, are commonly used for sampling from multivariate probability distributions. A long-sta…
Convergence Analysis of a Collapsed Gibbs Sampler for Bayesian Vector Autoregressions
Karl Oskar Ekvall, Galin L. Jones
We study the convergence properties of a collapsed Gibbs sampler for Bayesian vector autoregressions with predictors, or exogenous variables. The Markov chain generated by our algo…
Consistent Maximum Likelihood Estimation Using Subsets with Applications to Multivariate Mixed Models
Karl Oskar Ekvall, Galin L. Jones
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data t…
Multivariate Output Analysis for Markov chain Monte Carlo
Dootika Vats, James M. Flegal, Galin L. Jones
Markov chain Monte Carlo (MCMC) produces a correlated sample for estimating expectations with respect to a target distribution. A fundamental question is when should sampling stop…
Strong Consistency of Multivariate Spectral Variance Estimators
Dootika Vats, James M. Flegal, Galin L. Jones
Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution wh…
Markov Chain Monte Carlo Estimation of Quantiles
Charles Doss, James M. Flegal, Galin L. Jones +1
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Furt…
On the Geometric Ergodicity of Two-Variable Gibbs Samplers
Aixin Tan, Galin L. Jones, James P. Hobert
A Markov chain is geometrically ergodic if it converges to its in- variant distribution at a geometric rate in total variation norm. We study geo- metric ergodicity of deterministi…
Evaluating Default Priors with a Generalization of Eaton's Markov Chain
Brian P. Shea, Galin L. Jones
We consider evaluating improper priors in a formal Bayes setting according to the consequences of their use. Let be a class of functions on the parameter space and consider est…
Batch means and spectral variance estimators in Markov chain Monte Carlo
James M. Flegal, Galin L. Jones
Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MC…
Markov Chain Monte Carlo: Can We Trust the Third Significant Figure?
James M. Flegal, Murali Haran, Galin L. Jones
Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reporte…
Evaluation of Formal posterior distributions via Markov chain arguments
Morris L. Eaton, James P. Hobert, Galin L. Jones +1
We consider evaluation of proper posterior distributions obtained from improper prior distributions. Our context is estimating a bounded function of a parameter when the loss i…
Fixed-width output analysis for Markov chain Monte Carlo
Galin Jones, Murali Haran, Brian Caffo +1
Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a target distribution via ergodic averages. A fundamental question is when sh…
Sufficient burn-in for Gibbs samplers for a hierarchical random effects model
Galin L. Jones, James P. Hobert
We consider Gibbs and block Gibbs samplers for a Bayesian hierarchical version of the one-way random effects model. Drift and minorization conditions are established for the underl…