Efficiency of Markov chain Monte Carlo methods

随机漫步大都会（RWM）算法是一类重要的马尔可夫链蒙特卡罗（MCMC）算法，它是从高度复杂的概率分布（目标分布）中生成数据的方法。生物统计学、计算机科学、物理学、金融学和应用统计学等各个应用领域的研究人员和从业人员广泛使用这些方法。在应用RWM算法时，需要选择建议密度；由于其可及性，正常密度是最受欢迎的选择。为了使算法的性能达到某种程度的最优，必须仔细选择该分布的方差；这被称为最优缩放问题。关于这个问题的结果在具有独立分量的高维目标分布的文献中是可用的。

Random walk Metropolis (RWM) algorithms, an important class of Markov chain Monte Carlo (MCMC) algorithms, are methods to generate data from highly complex probability distributions (the target distribution). Researchers and practitioners in various fields of applications such as biostatistics, computer science, physics, finance, and applied statistics extensively use such methods. In applying RWM algorithms, it is necessary to choose a proposal density; due to its accessibility, the normal density is the most popular choice. The variance of this distribution must be selected carefully in order to have some level of optimality in the performance of the algorithm; this is called the optimal scaling problem. Results about this issue are available in the literature for high-dimensional target distributions with independent components.