On the background estimation by time slides in a network of gravitational wave detectors

TL;DR

This paper analyzes the limitations of the time slide method for background estimation in gravitational wave detector networks, showing that the false alarm rate error saturates with more time shifts, especially for detectors with different trigger rates.

Contribution

It provides explicit calculations demonstrating the saturation of background estimation error and highlights the limitations of the time slide method in certain detector configurations.

Findings

False alarm rate estimation error saturates with increasing time shifts.

Error saturation is significant for detectors with very different trigger rates.

Explicit computations for 2 and 3 detector networks illustrate the phenomenon.

Abstract

Time shifting the outputs of Gravitational Wave detectors operating in coincidence is a convenient way to estimate the background in a search for short duration signals. However this procedure is limited as increasing indefinitely the number of time shifts does not provide better estimates. We show that the false alarm rate estimation error saturates with the number of time shifts. In particular, for detectors with very different trigger rates this error saturates at a large value. Explicit computations are done for 2 detectors, and for 3 detectors where the detection statistic relies on the logical ``OR'' of the coincidences of the 3 couples in the network.