Inference with finite time series II: the window strikes back

TL;DR

This paper investigates the impact of window functions on gravitational-wave data analysis, revealing biases introduced by conventional methods and proposing a multi-stage approach for unbiased inference at high signal-to-noise ratios.

Contribution

It demonstrates that omitting power loss factors yields unbiased posteriors for moderate SNRs and introduces a multi-stage method for reliable likelihood estimation at higher SNRs.

Findings

Omitting the power loss factor leads to unbiased posteriors for SNRs up to ~100.

The proposed multi-stage method provides consistent likelihood estimates for SNRs up to ~1000.

Rectangular windows do not necessarily cause biased inference, contrary to common belief.

Abstract

Smooth window functions are often applied to strain data when inferring the parameters describing the astrophysical sources of gravitational-wave transients. Within the LIGO-Virgo-KAGRA collaboration, it is conventional to include a term to account for power loss due to this window in the likelihood function. We show that the inclusion of this factor leads to biased inference. The simplest solution to this, omitting the factor, leads to unbiased posteriors and Bayes factor estimates provided the window does not suppress the signal for signal-to-noise ratios $\lesssim O(100)$, but unreliable estimates of the absolute likelihood. Instead, we propose a multi-stage method that yields consistent estimates for the absolute likelihood in addition to unbiased posterior distributions and Bayes factors for signal-to-noise ratios $\lesssim O(1000)$. Additionally, we demonstrate that the commonly held wisdom that using rectangular windows necessarily leads to biased inference is incorrect.