标题： 在两种距离函数下对空间相关失效时间数据进行建模及其在Titan GPU数据中的应用 显示英文标题

标题： Modeling Spatially Correlated Failure-time Data Under Two Distance Functions with an Application to Titan GPU Data

摘要： 一种常见的空间相关数据统计分析方法依赖于仅基于未知参数和观测值位置之间的物理距离定义相关结构。 然而，一些数据具有复杂的 spatial 结构，仅用物理距离无法充分描述。 在本工作中，关注的空间失效时间数据包含通过网络结构拓扑连接的 GPU 信息，该拓扑不同于它们的物理布局，并且预期会引入额外的相关性。 所提出的寿命回归模型包括捕捉由于物理位置导致的依赖性的随机效应，以及解释由于 GPU 之间逻辑连接导致的依赖性的随机效应。 对这个 GPU 数据集的分析作为具有多个空间随机效应的模型示例，提出的想法可以扩展到其他具有复杂空间结构的应用。 推荐使用贝叶斯建模方案进行此类分析。 本工作中的示例使用软件包 Stan 来生成马尔可夫链蒙特卡洛抽样用于参数估计。 通过模拟验证了这种建模工作，结果展示了统计推断的准确性。 我们还将开发的框架应用于大规模 Titan GPU 失效时间数据。 显示英文摘要

摘要： One common approach to statistical analysis of spatially correlated data relies on defining a correlation structure based solely on unknown parameters and the physical distance between the locations of observed values. However, some data have a complex spatial structure that cannot be adequately described with the physical distance alone. In this work, the spatial failure-time data of focus contains information on GPUs that are connected through a network fabric topology that differs from their physical layout and that is expected to introduce additional correlations. The proposed lifetime regression model includes random effects capturing the dependency due to physical location as well as random effects explaining the dependency due to logical connections between GPUs. The analysis of this GPU dataset serves as an example of models with multiple spatial random effects and the ideas presented can be extended to other applications with complex spatial structures. A Bayesian modeling scheme is recommended for this class of analyses. The examples in this work use the software package, Stan, to produce Markov chain Monte Carlo draws for parameter estimation. This modeling effort is validated through simulation which demonstrates accuracy in statistical inference. We also apply the developed framework to the large-scale Titan GPU failure time data.