论文标题
在随机过程数据上发现最大差异的区域
Uncovering Regions of Maximum Dissimilarity on Random Process Data
论文作者
论文摘要
两个随机过程的局部特征的比较可以揭示该过程不同的时间或空间。本文提出了一种了解具有一定体积的区域的方法，其中两个过程的边际属性不那么相似。在关注数据本身就是随机过程的设置中，设计了所提出的方法，因此在功能数据，时间序列和点过程的背景下，所提出的方法可用于指出最大差异区域的最大差异区域。两个感兴趣的随机过程基础的参数函数是通过基础表示建模的，贝叶斯推断是通过集成的嵌套拉普拉斯近似进行的。数值研究验证了所提出的方法，我们通过有关犯罪学，金融和医学的案例研究展示了它们的应用。
The comparison of local characteristics of two random processes can shed light on periods of time or space at which the processes differ the most. This paper proposes a method that learns about regions with a certain volume, where the marginal attributes of two processes are less similar. The proposed methods are devised in full generality for the setting where the data of interest are themselves stochastic processes, and thus the proposed method can be used for pointing out the regions of maximum dissimilarity with a certain volume, in the contexts of functional data, time series, and point processes. The parameter functions underlying both stochastic processes of interest are modeled via a basis representation, and Bayesian inference is conducted via an integrated nested Laplace approximation. The numerical studies validate the proposed methods, and we showcase their application with case studies on criminology, finance, and medicine.
