Gibbs Samplers for Uniform Distributions: Uniform Ergodicity and an Adaptive Algorithm

Kovalevskii, Artyom (Novosibirsk, Russia)
pandorra@online.nsk.su

We prove that a Gibbs sampler for the uniform distribution on a bounded subset $G \subset { \mathbb R}^d$ is uniformly ergodic if G is ``not very sharp'', and it is not uniformly ergodic if, for some ${\mathbf x}$ in the boundary of G and all ${\mathbf y}\in G$, angles between ${\mathbf y-x}$ and coordinate axes are ``not very small''. We propose an adaptive algorithm in case if G is a rectangle in ${ \mathbb R}^2$.