Journée Richard Tweedie

Institut Henri Poincaré, Paris,   28 Janvier 2002

     Gareth O. Roberts

      Department of Statistics, Lancaster University, UK

     `One paper, three successes'
 The paper ``Rates of convergence in the Hastings and Metropolis algorithms'', Annals of Statistics, 1996, by Kerrie Mengersen and Richard Tweedie was the first paper written by Richard in the area of MCMC, but its influence on the subject has been far-reaching.

This talk will discuss the contributions contained in three of the main themes of this paper, and the way in which these results have influenced subsequent work in the area.

The three results consider

1. Necessary and sufficient conditions for geometric ergodicity of the Metropolis algorithm.

2. Necessary and sufficient conditions for geometric ergodicity of the Independence Sampler.

3. Computable bounds for convergence times of simple Metropolis-Hastings algorithms.