On the geometric ergodicity of hybrid samplers

In this paper, we consider the random scan symmetric random walk Metropolis algorithm (RSM) on R . This algorithm performs a Metropolis step on just one coordinate at a time (as opposed to the full dimensional symmetric Random walk Metropolis algorithm, which proposes a transition on all coordinates at once). We present various sucient conditions implying V -uniform ergodicity of the RSM when the target density decreases either sub-exponentially or exponentially in the tails. Keywords: Markov Chain Monte Carlo; Hybrid sampler; geometric ergodicity. AMS 1991 subject classi cation: 65C05, 60J10. G. Fort, (Corresponding author) LMC-IMAG, 51 rue des Mathematiques, B.P. 53, 38041 Grenoble Cedex 9, France E-mail: Gersende.Fort@imag.fr E. Moulines, ENST, 46, rue Barrault, 75634 Paris Cedex 13, France E-mail: moulines@tsi.enst.fr G.O.Roberts, Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK E-mail: G.O.Roberts@lancaster.ac.uk J.S. Rosenthal, Department of Statistics, University of Toronto, 100 St. George Street, Toronto, Ontario, Canada M5S 3G3 E-mail: je@math.toronto.edu 1