论文标题
关于使用本地$ \ hat {r} $改善MCMC收敛诊断
On the use of a local $\hat{R}$ to improve MCMC convergence diagnostic
论文作者
论文摘要
诊断马尔可夫链蒙特卡洛的收敛是至关重要的，并且基本上是一个未解决的问题。在最受欢迎的方法中，基于比较（基于比较）之间的比较，在最流行的降低因子（通常命名为$ \ hat {r} $）的指标中，可以监视输出链与目标分布的收敛性。自90年代引入以来，已经提出了一些改进。在这里，我们旨在通过提出一个局部版本的局部版本来更好地理解$ \ hat {r} $行为，该版本侧重于目标分布的分位数。该新版本依赖相关人群价值的关键理论属性。它自然会导致提出一个新的指标$ \ hat {r} _ \ infty $，这既可以在目标分布的不同分位数中本地将马尔可夫链蒙特卡洛收敛定位，同时处理其他$ \ hat {r} $ versions not contergence问题。
Diagnosing convergence of Markov chain Monte Carlo is crucial and remains an essentially unsolved problem. Among the most popular methods, the potential scale reduction factor, commonly named $\hat{R}$, is an indicator that monitors the convergence of output chains to a target distribution, based on a comparison of the between- and within-variances. Several improvements have been suggested since its introduction in the 90s. Here, we aim at better understanding the $\hat{R}$ behavior by proposing a localized version that focuses on quantiles of the target distribution. This new version relies on key theoretical properties of the associated population value. It naturally leads to proposing a new indicator $\hat{R}_\infty$, which is shown to allow both for localizing the Markov chain Monte Carlo convergence in different quantiles of the target distribution, and at the same time for handling some convergence issues not detected by other $\hat{R}$ versions.
