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Abstract : |
Abstract. We consider a Gibbs sampler applied to the uniform distribution on a bounded region R ? R d. We show that the convergence properties of the Gibbs sampler depend greatly on the smoothness of the boundary of R. Indeed, for sufficiently smooth boundaries the sampler is uniformly ergodic, while for jagged boundaries the sampler could fail to even be geometrically ergodic. 1. Introduction. This paper considers the use of Gibbs samplers applied to the uniform distribution on a bounded open region R ? R d. We shall show that, subject to C 2 smoothness of the boundary of R, such Gibbs samplers are always uniformly ergodic. We shall also show that, even with certain types of ?pointy ? boundaries, the Gibbs samplers are still geometrically, |
