标题： 区域保质量退火的最佳温度间隔 显示英文标题

标题： Optimal Temperature Spacing for Regionally Weight-preserving Tempering

摘要： 并行退火是允许MCMC算法正确探索$d$维多模态目标密度的流行方法。 传统基于功率的并行退火在多模态目标中存在一个问题，即与模式相关的概率质量比例可能随着不同的逆温度值而变化，有时甚至显著变化。 作者的补充工作提出了一种新颖的解决方案，涉及辅助目标，这些目标在提高密度时保留区域权重。 本文试图解决在使用这种权重保持方法时如何以最优方式选择温度间隔的问题。该问题在计算期望平方跳跃距离的可处理设置中进行了分析，然后可以针对调整参数进行优化。 结论是，对于一个适当构建的区域权重保持的退火算法，针对$d$维目标分布，连续温度间隔应表现为$\mathcal{O}\left(d^{-1/2}\right)$，这将导致温度交换移动的最优接受率位于区间$[0,0.234]$内。 显示英文摘要

摘要： Parallel tempering is popular method for allowing MCMC algorithms to properly explore a $d$-dimensional multimodal target density. One problem with traditional power-based parallel tempering for multimodal targets is that the proportion of probability mass associated to the modes can change for different inverse-temperature values, sometimes dramatically so. Complementary work by the authors proposes a novel solution involving auxiliary targets that preserve regional weight upon powering up the density. This paper attempts to address the question of how to choose the temperature spacings in an optimal way when using this type of weight-preserving approach.The problem is analysed in a tractable setting for computation of the expected squared jumping distance which can then be optimised with regards to a tuning parameter. The conclusion is that for an appropriately constructed regionally weight-preserved tempering algorithm targeting a $d$-dimensional target distribution, the consecutive temperature spacings should behave as $\mathcal{O}\left(d^{-1/2}\right)$ and this induces an optimal acceptance rate for temperature swap moves that lies in the interval $[0,0.234]$.