Sufficient burn-in for Gibbs samplers for a hierarchical random effects model
Galin L. Jones, James P. Hobert
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. 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.
Create a lesson
Related papers
Sampling with collective variables: Relative error analysis for umbrella sampling under general conditions
Holden Lee, Matheau Santana-Gijzen, Jonathan Weare
Inference for Fréchet Mean Sets
Ryunosuke Miyazaki
Minimax rates for pointwise CATE estimation: the role of design smoothness
Yuxuan Hou, Zhenghan Li
A pedestrian's approach to Bayesian methods for inverse problems
Heiko Gimperlein, Michael Oberguggenberger
Interpolation and coherence in multiple testing
Ninh Tran, Dennis Leung, Jesse Hemerik
A new approach for estimating the number of spikes in high-dimensional Gaussian models
Hugo Jeannin, Pascal Vallet, Florent Bouchard et al.