Reversible Jump MCMC Converging to Birth-and-Death MCMC and More General Continuous Time Samplers

@inproceedings{Capp2001ReversibleJM,
  title={Reversible Jump MCMC Converging to Birth-and-Death MCMC and More General Continuous Time Samplers},
  author={Olivier Capp{\'e} and Tobias Ryd{\'e}n},
  year={2001}
}
At present, reversible jump methods are the most common tool for exploring variable dimension statistical models. Recently however, an alternative approach based on birth-and-death processes has been proposed in the case of mixtures of distributions by Stephens (2000). We address the comparison of both methods by demonstrating that upon appropriate rescaling of the time axis, the reversible jump chain converges to a limiting continuous time birth-and-death chain. We show in addition that the… CONTINUE READING

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