Espinosa Sebastián, Silva Jorge F, Céspedes Sandra
Department of Electrical Engineering, Universidad de Chile, Santiago 9170022, Chile.
Department of Computer Science & Software Engineering, Concordia University, Montreal, QC H3G 1M8, Canada.
Entropy (Basel). 2024 Jul 12;26(7):596. doi: 10.3390/e26070596.
A central challenge in hypothesis testing (HT) lies in determining the optimal balance between Type I (false positive) and Type II (non-detection or false negative) error probabilities. Analyzing these errors' exponential rate of convergence, known as error exponents, provides crucial insights into system performance. Error exponents offer a lens through which we can understand how operational restrictions, such as resource constraints and impairments in communications, affect the accuracy of distributed inference in networked systems. This survey presents a comprehensive review of key results in HT, from the foundational to recent advancements in distributed HT, all unified through the framework of error exponents. We explore asymptotic and non-asymptotic results, highlighting their implications for designing robust and efficient networked systems, such as event detection through lossy wireless sensor monitoring networks, collective perception-based object detection in vehicular environments, and clock synchronization in distributed environments, among others. We show that understanding the role of error exponents provides a valuable tool for optimizing decision-making and improving the reliability of networked systems.
假设检验（HT）中的一个核心挑战在于确定第一类错误（误报）和第二类错误（未检测到或漏报）概率之间的最佳平衡。分析这些错误的指数收敛速率，即所谓的错误指数，能为系统性能提供关键见解。错误指数提供了一个视角，通过它我们可以理解诸如资源限制和通信损伤等操作限制如何影响网络系统中分布式推理的准确性。本综述全面回顾了假设检验的关键成果，从基础内容到分布式假设检验的最新进展，所有这些都通过错误指数框架统一起来。我们探讨了渐近和非渐近结果，强调了它们对设计健壮且高效的网络系统的意义，例如通过有损无线传感器监测网络进行事件检测、车辆环境中基于集体感知的目标检测以及分布式环境中的时钟同步等。我们表明，理解错误指数的作用为优化决策和提高网络系统的可靠性提供了一个有价值的工具。
