Nonparametric distributed detection using bootstrapping and fisher's method

This paper addresses the problem of distributed decision making when there is no or very vague knowledge about the probability models associated with the hypotheses. Such scenarios occur for example in the Internet of Things (IoT), data analytics, radio spectrum monitoring, sensor networks, environmental surveillance. It may not be feasible to specify accurate probability models needed in inference for a large number of distributed sensors. The probability models are learned from the data via empirical distributions that provide an accurate approximation of the true model. The bootstrap method is employed to approximate the distributions with high accuracy. The Anderson-Darling test is employed in each sensor and the computed p-values are communicated to the Fusion Center (FC) that makes the final decision. The FC employs the Fisher's method to fuse the local p-values. The decision is based on the distribution of p-values instead of actual p-values. The proposed method detects changes in probability model even if the distributions differ only slightly. Numerical simulations demonstrate that the Fisher's method evaluating the distribution of obtained local p-values consistently outperforms widely used Boolean fusion rules.