Sky Localization and Parameter Estimation

Immediately after one of the search pipelines reports an event, sky localization and parameter estimation analyses begin. These analyses all use Bayesian inference to calculate the posterior probability distribution over the parameters (sky location, distance, and/or intrinsic properties of the source) given the observed gravitational-wave signal.

There are different parameter estimation methods for modeled (CBC) and unmodeled (burst) events. However, in both cases there is a rapid analysis that estimates only the sky localization, and is ready in seconds, and a refined analysis that explores a larger parameter space and completes up to hours or a day later.

Modeled Events

BAYESTAR [1] is the rapid CBC sky localization algorithm. It reads in the matched-filter time series from the search pipeline and calculates the posterior probability distribution over the sky location and distance of the source by coherently modeling the response of the gravitational-wave detector network. It explores the parameter space using Gaussian quadrature, lookup tables, and sampling on an adaptively refined HEALPix grid. The sky localization takes tens of seconds and is included in the preliminary alert.

LALInference [2] is a full CBC parameter estimation pipeline. It explores a greatly expanded parameter space including sky location, distance, masses, and spins, and performs full forward modeling of the gravitational-wave signal and the strain calibration of the gravitational-wave detectors. It explores the parameter space using MCMC and nested sampling. For all events, there is an automated LALInference analysis that uses the least expensive CBC waveform models and completes within hours and may be included in a subsequent alert. More time-consuming analyses with more sophisticated waveform models are started at the discretion of human analysts, and will complete days or weeks later.

Bilby [3] is a next-generation python-based Bayesian inference parameter estimation code. Bilby provides a user-friendly and accessible interface with the latest stochastic sampling methods built-in. It can be used for gravitational-wave analyses to extract source properties of CBC events such as masses, spins, distance and sky location. These parameters are extracted by employing the use of stochastic sampling methods such as MCMC and nested sampling. An automated pipeline is used to perform a Bilby analysis on all CBC events. The automated parameter estimation pipeline uses less expensive default settings, including the use of simpler waveforms, to perform an initial analysis of the event. Further analyses with more complex waveforms are performed by a human analyst as needed.

Unmodeled Events

cWB, the burst search pipeline, also performs a rapid sky localization based on its coherent reconstruction of the gravitational-wave signal using a wavelet basis and the response of the gravitational-wave detector network [4]. The cWB sky localization is included in the preliminary alert.

Refined sky localizations for unmodeled bursts are provided by two algorithms that use the same MCMC and nested sampling methodology as LALInference. LALInference Burst (LIB) [5] models the signal as a single sinusoidally modulated Gaussian. BayesWave [6] models the signal as a superposition of wavelets and jointly models the background with both a stationary noise component and glitches composed of wavelets that are present in individual detectors.