We consider a parallel decentralized detection system employing a bank of local detectors (LDs) to access a commonly-observed phenomenon. The system makes a binary decision about the phenomenon, accepting one of two hypotheses ( $H_{0}$ (“absent”) or $H_{1}$ (“present”)). The $k$ th LD uses a local decision rule to compress its local observations $y_{k}$ into a binary local decision $u_{k};\ u_{k}=0$ if the $k$ th LD accepts $H_{0}$ and $u_{k}=1$ if it accepts $H_{1}$ . The $k$ th LD sends its decision $u_{k}$ over a noiseless dedicated channel to a Data Fusion Center (DFC). The DFC combines the local decisions it receives from $n$ LDs ( $u_{1}, u_{2},\ldots, u_{n}$ ) into a single binary global decision $u_{0} (u_{0}=0$ for accepting $H_{0}$ or $u_{0}=1$ for accepting $H_{1}$ ). If each LD uses a single deterministic local decision rule (calculating $u_{k}$ from the local observations $y_{k}$ ) and the DFC uses a single deterministic global decision rule (calculating $u_{0}$ from the $n$ local decisions), the team receiver operating characteristic (ROC) curve is in general non-concave. The system's performance under a Neyman-Pearson criterion may then be suboptimal in the sense that a mixed strategy may yield a higher probability of detection when the probability of false alarm is constrained not to exceed a certain value, $\alpha > 0$ . Specifically, a “dependent randomization” detection scheme can be applied in certain circumstances to improve the system's performance by making the ROC curve concave. This scheme requires a coordinated and synchronized action between the DFC and the LDs. In this study, we specify when dependent randomization is needed, and discuss the proper response of the detection system if synchronization between the LDs and the DFC is temporarily lost.

中文翻译：

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并行二元决策融合中的相依随机化

我们考虑使用一组本地检测器（LD）来访问常见现象的并行分散式检测系统。系统针对该现象做出二元决策，接受两个假设之一（ $ H_ {0} $ （“缺席”）或 $ H_ {1} $（“当下”））。的$ k $ LD使用本地决策规则压缩其本地观测值 $ y_ {k} $ 转化为二进制的本地决策 $ u_ {k}; \ u_ {k} = 0 $ 如果 $ k $ LD接受 $ H_ {0} $ 和 $ u_ {k} = 1 $ 如果接受 $ H_ {1} $ 。的$ k $ LD发送决定 $ u_ {k} $通过无噪音的专用通道到达数据融合中心（DFC）。DFC合并了从DFC收到的本地决策$ n $ LDs（ $ u_ {1}，u_ {2}，\ ldots，u_ {n} $ ）转换为单个二进制全局决策 $ u_ {0}（u_ {0} = 0 $ 接受 $ H_ {0} $ 要么 $ u_ {0} = 1 $ 接受 $ H_ {1} $ ）。如果每个LD使用单个确定性本地决策规则（计算$ u_ {k} $ 从当地观察 $ y_ {k} $ ），而DFC使用单个确定性全局决策规则（计算 $ u_ {0} $ 来自 $ n $本地决策），团队接收者的工作特征（ROC）曲线通常是不凹的。从某种意义上说，在错误警报的概率被限制为不超过某个特定值的情况下，混合策略可能会产生更高的检测概率，因此在Neyman-Pearson准则下系统的性能可能不是最佳的，$ \ alpha> 0 $ 。具体而言，可以在某些情况下应用“依赖随机化”检测方案，以通过使ROC曲线凹入来提高系统性能。该方案要求DFC与LD之间采取协调一致的动作。在这项研究中，我们指定了何时需要依赖随机化，并讨论了如果LD和DFC之间的同步暂时丢失，则检测系统的正确响应。