Gravitational wave detection without boot straps: A Bayesian approach

Abstract

In order to separate astrophysical gravitational-wave signals from instrumental noise, which often contains transient non-Gaussian artifacts, astronomers have traditionally relied on bootstrap methods such as time slides. Bootstrap methods sample with replacement, comparing single-observatory data to construct a background distribution, which is used to assign a false-alarm probability to candidate signals. While bootstrap methods have played an important role establishing the first gravitational-wave detections, there are limitations. First, as the number of detections increases, it makes increasingly less sense to treat single-observatory data as bootstrap-estimated noise, when we know that the data are filled with astrophysical signals, some resolved, some unresolved. Second, it has been known for a decade that background estimation from time-slides eventually breaks down due to saturation effects, yielding incorrect estimates of significance. Third, the false alarm probability cannot be used to weight candidate significance, for example when performing population inference on a set of candidates. Given recent debate about marginally resolved gravitational-wave detection claims, the question of significance has practical consequences. We propose a Bayesian framework for calculating the odds that a signal is of astrophysical origin versus instrumental noise without bootstrap noise estimation. We show how the astrophysical odds can safely accommodate glitches. We argue that it is statistically optimal. We demonstrate the method with simulated noise and provide examples to build intuition about this new approach to significance.

Search for strongly lensed counterpart images of binary black hole mergers in the first two LIGO observing runs

“…The optimal method to identify lensed counterpart images of a GW observation would be to perform Bayesian inference on the full dataset [24]. This would need to include prior knowledge of the rate and properties of counterpart images given the information known about the GW signal.…”

A search for intermediate-mass black holes mergers in the second LIGO--Virgo observing run with the Bayes Coherence Ratio

“…This method relies on accurate models for the signal and glitch morphologies [70]. In principle, Bayesian odds is the optimal method for hypothesis testing [71]. Much of its power comes from the Bayesian evidence, the likelihood of the data given a hypothesis.…”

“…Although a significant fraction of the glitches can be identified by testing them for coherence amongst two or more detectors and performing matched-filtering, these methods are insufficient to identify all glitches [65][66][67]. One method to discriminate more glitches while searching for CBCs is the Bayesian odds [68][69][70][71][72][73]. The Bayesian Coherence Ratio ρ BCR [70,71] is a Bayesian odds comparing the probability that the data contains coherent signals vs. incoherent glitches.…”

“…One method to discriminate more glitches while searching for CBCs is the Bayesian odds [68][69][70][71][72][73]. The Bayesian Coherence Ratio ρ BCR [70,71] is a Bayesian odds comparing the probability that the data contains coherent signals vs. incoherent glitches. In this paper, we use the ρ BCR to rank O2's coincident CBC gravitationalwave candidates with lab-frame total masses in the range of 55 − 500 M .…”

When models fail: an introduction to posterior predictive checks and model misspecification in gravitational-wave astronomy

“…• Bootstrapping methods-in which real data is used as a sampling distribution for synthetic data-can often be helpful for diagnosing noise misspecification. In gravitational-wave astronomy, data residuals can be bootstrapped to create new noise realisations; this method was integral to the first gravitational-wave detections Cannon et al (2013Cannon et al ( , 2015; Ashton et al (2019). New noise realisations may also be generated from existing data using methods like time-sliding or time reversal.…”