Using the Moreau-Yosida envelope density as an importance distribution yields an asymptotically normal, finite-variance Markov chain importance sampling estimator that often beats proximal MALA and HMC.
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MCMC Importance Sampling via Moreau-Yosida Envelopes
Using the Moreau-Yosida envelope density as an importance distribution yields an asymptotically normal, finite-variance Markov chain importance sampling estimator that often beats proximal MALA and HMC.