Optimal Proposal Distributions and Adaptive MCMC

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Kernel Sequential Monte Carlo (2015, methodology): “We now review how these quantities were previously modelled using kernel methods in the context of MCMC. Note that any form of adaptation in MCMC requires care in order to preserve ergodicity of the resulting Markov chain, and some form of vanishing adaptation is needed [1, 18].”
Model choice using reversible jump Markov chain Monte Carlo (2012, methodology): “Rosenthal (2011) provides an introduction to this approach, including the assumptions required for the validity of the approach.”
Component-Wise Markov Chain Monte Carlo: Uniform and Geometric Ergodicity under Mixing and Composition (2009, methodology): “This has led to investigation of optimal scaling of Metropolis algorithms and so-called adaptive algorithms which allow the proposal kernel to change over the course of the simulation (see, e.g., Bédard and Rosenthal, 2008; Rosenthal, 2011).”
Direct parametric reconstruction from undersampled (k, t)-space data in dynamic contrast enhanced MRI (2014, background): “Although the selection of proposal density is not trivial and can affect convergence (Rosenthal, 2010), normal proposal distributions usually work well in practice and this is why they were chosen in this scheme.”