🤖 AI Summary
研究解决了轻尾目标分布下Metropolis接受率不稳定的问题，通过无梯度随机游走Metropolis采样方法，在合理选择提议方差时保持了稳定的接受概率。
📝 Abstract
In Markov chain Monte Carlo sampling, light-tailed target distributions present something of a poisoned chalice: their light tails offer good confinement, and tend to imply good mixing properties for natural continuous-time dynamics, but the steepness of their tail decay means that they often fall outside of the scope of modern quantitative convergence theory. For usual gradient-based samplers, this reflects a genuine instability issue, whereby Metropolis acceptance rates can degrade badly. In this work, we study the gradient-free random-walk Metropolis sampler, and show that for a wide range of light-tailed targets, the acceptance probability remains stable for reasonable choices of proposal variance, from which effective and favourable mixing time estimates can be deduced. The analysis relies on a simple relationship between the first and second derivatives of the log-density of the target distribution.