Multiple Hypothesis Testing Framework for Spatial Signals

TL;DR

This paper introduces a flexible multiple hypothesis testing framework for spatial signals, enabling the identification of interesting regions in large sensor networks while controlling false discoveries, applicable to various physical phenomena.

Contribution

It presents a novel, data-driven approach to estimate local false discovery rates using spectral methods, independent of specific spatial propagation models.

Findings

Effective identification of spatial regions with interesting behavior.

Controlled false discovery rate in large sensor networks.

Application to radio wave propagation demonstrates practical utility.

Abstract

The problem of identifying regions of spatially interesting, different or adversarial behavior is inherent to many practical applications involving distributed multisensor systems. In this work, we develop a general framework stemming from multiple hypothesis testing to identify such regions. A discrete spatial grid is assumed for the monitored environment. The spatial grid points associated with different hypotheses are identified while controlling the false discovery rate at a pre-specified level. Measurements are acquired using a large-scale sensor network. We propose a novel, data-driven method to estimate local false discovery rates based on the spectral method of moments. Our method is agnostic to specific spatial propagation models of the underlying physical phenomenon. It relies on a broadly applicable density model for local summary statistics. In between sensors, locations are assigned to regions associated with different hypotheses based on interpolated local false discovery rates. The benefits of our method are illustrated by applications to spatially propagating radio waves.