Reversible jump, birth‐and‐death and more general continuous time Markov chain Monte Carlo samplers

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Towards Automatic Model Comparison: An Adaptive Sequential Monte Carlo Approach (2013, methodology): “Sophisticated variants of these algorithms, such as those developed in Peters et al. (2010), have been considered in recent years but depend upon essentially the same construction and ultimately require adequate mixing of the underlying Markov process.”
Population Monte Carlo (2004, methodology): “Indeed, while adaptive importan e sampling strategies have already been onsidered in the pre-MCMC area, as in, e.g., Oh and Berger (1992,1993), the MCMC environment is mu h harsher for adaptive algorithms, be ause the adaptivity an els the Markovian nature of the sequen e and thus alls for more elab”