# Noise residuals for GW150914 using maximum likelihood and numerical relativity templates

## TL;DR

This paper critically reexamines the noise residuals in GW150914, revealing that previous reductions in correlations were due to template issues and biases, emphasizing the need for careful analysis in gravitational wave data.

## Contribution

The study identifies flaws in the maximum likelihood template approach and demonstrates how proper rematching affects residual correlation assessments.

## Key findings

- Rematching the ML template restores residual correlations to 60% of previous levels.
- Correcting biases reduces the significance probability by over an order of magnitude.
- The ML template used previously is problematic, affecting the interpretation of residual correlations.

## Abstract

We reexamine the results presented in a recent work by Nielsen et al. [1], in which the properties of the noise residuals in the 40\,ms chirp domain of GW150914 were investigated. This paper confirmed the presence of strong (i.e., about 0.80) correlations between residual noise in the Hanford and Livingston detectors in the chirp domain as previously seen by us [2] when using a numerical relativity template given in [3]. It was also shown in [1] that a so-called maximum likelihood template can reduce these statistically significant cross-correlations. Here, we demonstrate that the reduction of correlation and statistical significance is due to (i) the use of a peculiar template which is qualitatively different from the properties of GW150914 originally published by LIGO, (ii) a suspicious MCMC chain, (iii) uncertainties in the matching of the maximum likelihood (ML) template to the data in the Fourier domain, and (iv) a biased estimation of the significance that gives counter-intuitive results. We show that rematching the maximum likelihood template to the data in the 0.2\,s domain containing the GW150914 signal restores these correlations at the level of $60\%$ of those found in [1]. With necessary corrections, the probability given in [1] will decrease by more than one order of magnitude. Since the ML template is itself problematic, results associated with this template are illustrative rather than final.