论文标题
大都会蒙特卡洛抽样：收敛，定位过渡和最佳性
Metropolis Monte Carlo sampling: convergence, localization transition and optimality
论文作者
论文摘要
在随机抽样方法中，马尔可夫链蒙特卡洛算法是最重要的。在随机行走都会议方案中，我们利用分析方法和数值方法的结合研究了它们的收敛性能。分析某些模型算法的放松特性足够简单以实现分析性进度，我们表明，与目标稳态分布的偏差可以以定位的特征长度的函数为定位过渡，以定义随机步行的特征长度。虽然蒙特卡洛算法的迭代趋向于所有选择跳跃参数的均衡，但本地化过渡在算法的有限步骤和靶平衡分布之后，差异分布之间差异的差异形状发生了巨大变化。我们认为，本地化过渡之前和之后的放松分别受扩散和排斥率的限制。
Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis scheme. Analysing the relaxation properties of some model algorithms sufficiently simple to enable analytic progress, we show that the deviations from the target steady-state distribution can feature a localization transition as a function of the characteristic length of the attempted jumps defining the random walk. While the iteration of the Monte Carlo algorithm converges to equilibrium for all choices of jump parameters, the localization transition changes drastically the asymptotic shape of the difference between the probability distribution reached after a finite number of steps of the algorithm and the target equilibrium distribution. We argue that the relaxation before and after the localisation transition is respectively limited by diffusion and rejection rates.
