论文标题
MCMC模拟中的配置与回火算法的几何优化之间的距离
Distance between configurations in MCMC simulations and the geometrical optimization of the tempering algorithms
论文作者
论文摘要
对于给定的马尔可夫链蒙特卡洛（MCMC）算法，我们定义了量化过渡难度的配置之间的距离。这个距离使我们能够以几何方式研究MCMC算法，我们研究了针对具有高度退化真空的极度多模式系统实施的模拟回火算法的几何形状。我们表明，扩展配置空间的大规模几何形状由渐近的反DE保姆度量给出，并以一种简单的几何方式争论，应最好地将回火参数定为指数置，以使高维度的过渡率获得高接收率。我们还讨论了钢化Lefschetz Thimble方法的几何优化，该方法是解决数值符号问题的算法。
For a given Markov chain Monte Carlo (MCMC) algorithm, we define the distance between configurations that quantifies the difficulty of transitions. This distance enables us to investigate MCMC algorithms in a geometrical way, and we investigate the geometry of the simulated tempering algorithm implemented for an extremely multimodal system with highly degenerate vacua. We show that the large scale geometry of the extended configuration space is given by an asymptotically anti-de Sitter metric, and argue in a simple, geometrical way that the tempering parameter should be best placed exponentially to acquire high acceptance rates for transitions in the extra dimension. We also discuss the geometrical optimization of the tempered Lefschetz thimble method, which is an algorithm towards solving the numerical sign problem.
