Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise. II: Bayesian analyses

TL;DR

This paper introduces a Bayesian approach to detect gravitational waves in non-Gaussian noise, confirming previous methods and automatically removing problematic auto-correlation terms for stochastic signals.

Contribution

It provides a Bayesian derivation of non-Gaussian noise detection techniques, simplifying the process and improving the handling of stochastic signals.

Findings

Bayesian probability closely matches previous detection statistic.

Auto-correlation term automatically eliminated for stochastic signals.

Method effective in weak signal, high SNR regimes.

Abstract

In a previous paper (gr-qc/0105100) we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by truncating sample values which lie in those non-Gaussian tails. The methods were derived, in the frequentist framework, by minimizing false alarm probabilities at fixed false detection probability in weak signal limit. For stochastic signals, the resulting statistic consisted of a sum of an auto-correlation term and a cross-correlation term; it was necessary to discard by hand the auto-correlation term to obtain the correct, generalized cross-correlation statistic. In the present paper, we present an alternative Bayesian derivation of the same signal detection techniques. We compute the probability that a signal is present in the data, in the limit where the signal-to-noise ratio squared per frequency bin is small, where the integrated signal-to-noise ratio is large compared to one, and where the total probability in the non-Gaussian tail part of the noise distribution is small. We show that, for each model considered, the resulting probability is to a good approximation a monotonic function of the detection statistic derived in the previous paper. Moreover, for stochastic signals, the new Bayesian derivation automatically eliminates the problematic auto-correlation term.