Uniform ergodicity and spectral gap of importance-tempered MCMC with heavy-tailed targets

2026-10-26来源 arXiv stat.COEnglish

arXiv:2506.19186v2 Announce Type: replace Abstract: We study the importance-tempered random-walk Metropolis (RWM) algorithm on $\mathbb{R}^d$, which targets the tempered density $\pi_\beta(x) \propto \pi(x)^\beta$ with $\beta \in (0,1)$ and corrects for the resulting bias by importance weighting. The dynamics of this sampler can be described by a continuous-time Markov chain whose embedded chain is the tempered RWM. We prove that when the tails of $\pi$ decay at rate $\|x\|^{-\gamma}$, this continuous-time chain is uniformly ergodic if and only if $d/\gamma

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Uniform ergodicity and spectral gap of importance-tempered MCMC with heavy-tailed targets

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