Determining the quality of sensing devices exhibiting minimal digitization complexity is addressed. Measurements of such sensor systems are characterized by multivariate binary distributions and assessing sensitivity via the Cramér-Rao lower bound turns out to be intractable. In this context, the Fisher matrix of the exponential family and a lower bound for arbitrary probabilistic models are discussed. The conservative approximation for Fisher’s information matrix rests on a surrogate exponential family distribution connected to the actual data-generating system by two compact equivalences. Without characterizing the likelihood and its support, this probabilistic notion enables designing estimators that consistently achieve the sensitivity level defined by the inverse of the conservative information matrix. For hard-limited multivariate Gaussian signal models, a quadratic exponential surrogate distribution tames statistical complexity such that a quantitative and conservative assessment of Fisher information becomes possible. This result is exploited for the Fisherian quantization loss analysis of an array with low-complexity binary sensors in comparison to an ideal system featuring infinite amplitude resolution. Additionally, data-driven assessment by estimating a conservative approximation for the Fisher matrix under recursive binary sampling as implemented in ΣΔ-modulating analog-to-digital converters is demonstrated.

中文翻译：

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通过定量 Fisher 信息下界对二元采样系统进行灵敏度分析

解决了确定表现出最小数字化复杂性的传感设备的质量问题。这种传感器系统的测量以多元二元分布为特征，并且通过 Cramér-Rao 下限评估灵敏度被证明是棘手的。在此背景下，讨论了指数族的 Fisher 矩阵和任意概率模型的下界。Fisher 信息矩阵的保守近似基于通过两个紧凑等价连接到实际数据生成系统的代理指数族分布。在不表征可能性及其支持的情况下，这种概率概念能够设计出能够始终达到由保守信息矩阵的逆定义的灵敏度水平的估计器。对于硬限制多元高斯信号模型，二次指数代理分布可以抑制统计复杂性，从而可以对 Fisher 信息进行定量和保守的评估。与具有无限幅度分辨率的理想系统相比，该结果可用于具有低复杂度二进制传感器的阵列的 Fisher 量化损失分析。此外，还展示了通过在 ΣΔ 调制模数转换器中实现的递归二进制采样下估计 Fisher 矩阵的保守近似来进行数据驱动的评估。与具有无限幅度分辨率的理想系统相比，该结果可用于具有低复杂度二进制传感器的阵列的 Fisher 量化损失分析。此外，还展示了通过在 ΣΔ 调制模数转换器中实现的递归二进制采样下估计 Fisher 矩阵的保守近似来进行数据驱动的评估。与具有无限幅度分辨率的理想系统相比，该结果可用于具有低复杂度二进制传感器的阵列的 Fisher 量化损失分析。此外，还展示了通过在 ΣΔ 调制模数转换器中实现的递归二进制采样下估计 Fisher 矩阵的保守近似来进行数据驱动的评估。