Geometric ergodicity of Metropolis algorithms

Ln this paper we derive conditions for geometric ergodicity of the random-walk-based Metropolis algorithm on R-k. We show that at least exponentially light tails of the target density is a necessity. This extends the one-dimensional result of Mengersen and Tweedle (1996, Arm. Statist. 24, 101-121). For super-exponential target densities we characterize the geometrically ergodic algorithms and we derive a practical sufficient condition which is stable under addition and multiplication. This condition is especially satisfied for the class of densities considered in Roberts and Tweedle (1996, Biometrika 83, 95-110). (C) 2000 Elsevier Science B.V. All rights reserved.