|CLAUDE BELISLE, Département de mathématiques et statistique, Université de Laval, Montréal, Québec G1K 7P4, Canada|
|The Hit-and-run sampler|
The hit-and-run sampler is a Markov Chain Monte Carlo method for simulating probability measures.
Let be an absolutely continuous probability measure on . Let be a full dimensional probability measure on the surface S of the d-dimensional unit ball centered at the origin. Given a current point , the hit-and-run sampler chooses a next point Xn+1 according to the conditionalization of on the line through Xn and . The directions are independent and identically distributed on S, with distribution . Under an appropriate irreducibility condition, the Markov chain converges in total variation towards the target distribution . In this talk, I will discuss the convergence properties of this Markov chain. Related Markov Chain Monte Carlo methods, including the Gibbs sampler, will also be discussed.