Abstract
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. hese 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.
Original language | English (US) |
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Pages (from-to) | 784-817 |
Number of pages | 34 |
Journal | Annals of Statistics |
Volume | 32 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2004 |
Keywords
- Block Gibbs sampler
- Burn-in
- Convergence rate
- Drift condition
- Geometric ergodicity
- Markov chain
- Minorization condition
- Monte Carlo
- Total variation distance