2004/04/01 by Galin L. Jones, James P. Hobert · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #Bayesian Methods and Mixture Models #Markov Chains and Monte Carlo Methods #math.ST #msc:60J10 #msc:62F15 #stat.TH
paper · pdf · doi:10.1214/009053604000000184
published as Annals of Statistics 2004, Vol. 32, No. 2, 784-817
openalex publication_date 2004/04/01 · arxiv created 2004/06/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 underlying Markov chains. The drift and minorization are used in conjunction with results from J. S. Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558–566] and G. O. Roberts and R. L. Tweedie [Stochastic Process. Appl. 80 (1999) 211–229] to construct analytical upper bounds on the distance to stationarity. These lead to upper bounds on the amount of burn-in that is required to get the chain within a prespecified (total variation) distance of the stationary distribution. The results are illustrated with a numerical example.