Randomizing the Metropolis-Hastings step size preserves spectral gaps and algorithmic complexity while making mixing degrade polynomially, not exponentially, when the step size is mis-tuned.
Ann Statist 49(4):1958–1981
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On randomized step sizes in Metropolis-Hastings algorithms
Randomizing the Metropolis-Hastings step size preserves spectral gaps and algorithmic complexity while making mixing degrade polynomially, not exponentially, when the step size is mis-tuned.