Convergence rates of two-component MCMC samplers

Two convergence properties of hybrid samplers

Theoretical work on Markov chain Monte Carlo (MCMC) algorithms has so far mainly concentrated on the properties of simple algorithms such as the Gibbs sampler, or the full-dimensional Hastings-Metropolis algorithm. In practice, these simple algorithms are used as building blocks for more sophisticated methods, which we shall refer to as hybrid samplers. It is often hoped that good convergence p...

On convergence rates of Gibbs samplers for uniform distributionsbyGareth

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 suuciently smooth boundaries the sampler is uniformly ergodic, while for jagged boundaries the sampler could fail to even be geometrically ergodic.

On Convergence Rates of Gibbs Samplers for Uniform Distributions

We consider a Gibbs sampler applied to the uniform distribution on a bounded region R ⊆ R. 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.

Asymptotic Variance and Convergence Rates of Nearly-Periodic MCMC Algorithms

Lower Bounds on the Convergence Rates of Adaptive Mcmc Methods

We consider the convergence properties of recently proposed adaptive Markov chain Monte Carlo (MCMC) algorithms for approximation of high-dimensional integrals arising in Bayesian analysis and statistical mechanics. Despite their name, in the general case these algorithms produce non-Markovian, time-inhomogeneous, irreversible stochastic processes. Nevertheless, we show that lower bounds on the...