Applications of distance between probability distributions to gravitational wave data analysis

TL;DR

This paper introduces a new probability distribution distance based on the L1 norm, compares it with existing measures, and explores its applications in gravitational wave data analysis tasks such as template placement and signal resolution.

Contribution

It proposes a novel L1-based distance measure for probability distributions and evaluates its potential in gravitational wave data analysis contexts.

Findings

The L1 distance offers a new way to compare probability distributions.

The measure is compared with Kullback-Leibler divergence and Fisher matrix-based distance.

Potential applications include template placement and signal resolution in gravitational wave searches.

Abstract

We present a definition of the distance between probability distributions. Our definition is based on the $L_1$ norm on space of probability measures. We compare our distance with the well-known Kullback-Leibler divergence and with the proper distance defined using the Fisher matrix as a metric on the parameter space. We consider using our notion of distance in several problems in gravitational wave data analysis: to place templates in the parameter space in searches for gravitational-wave signals, to assess quality of search templates, and to study the signal resolution.