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MALA with annealed proposals: a generalization of locally and globally balanced proposal distributions

机译：MALA with annealed proposals: a generalization of locally and globally balanced proposal distributions

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摘要

We introduce a generalized version of the Metropolis-adjusted Langevin algorithm (MALA). The informed proposal distribution of this new sampler features two tuning parameters: the usual step size parameter sigma(2) and an interpolation parameter. that may be adjusted to accommodate the dimension of the target distribution. We theoretically study the efficiency of the sampler by making use of the local- and global-balance concepts introduced in Zanella (JASA 115:852-865, 2020) and provide efficient tuning guidelines that work well with a variety of target distributions. Although the usual MALA (gamma = 1) is shown to be optimal for infinite-dimensional targets, in practice, the generalized MALA (1 gamma = 2) remains the most appealing option, even in high-dimensional contexts. Simulation studies and numerical experiments are presented to illustrate our findings. We apply the new sampler to a Bayesian logistic regression context and show that its efficiency compares favourably to competing algorithms.

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