Convergence of conditional metropolis-hastings samplers

We consider Markov chain Monte Carlo algorithms which combine Gibbs updates with Metropolis-Hastings updates, resulting in a conditional Metropolis-Hastings sampler (CMH sampler). We develop conditions under which the CMH sampler will be geometrically or uniformly ergodic. We illustrate our results by analysing aCMHsampler used for drawing Bayesian inferences about the entire sample path of a diffusion process, based only upon discrete observations.