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Convergence of conditional Metropolis-Hastings samplers. (English) Zbl 1379.60082
Summary: 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 a CMH sampler used for drawing Bayesian inferences about the entire sample path of a diffusion process, based only upon discrete observations.

MSC:
60J22 Computational methods in Markov chains
60J05 Discrete-time Markov processes on general state spaces
65C05 Monte Carlo methods
62F15 Bayesian inference
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