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.

Bilby [2] is a full CBC parameter estimation pipeline in Python. Bilby provides a user-friendly and accessible interface with the latest stochastic sampling methods built-in. 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 stochastic sampling methods such as MCMC and nested sampling. For all events, there is an automated Bilby analysis whose settings depend on the initial estimate of chirp mass from the search pipeline. The table below summarizes the waveform model and spin prior employed for parameter estimation. The analysis is accelerated with the reduced order quadrature basis elements constructed for the employed waveform models [9], and completes within tens of minutes for BNS and hours for NSBH and BBH.

RapidPE-RIFT [3] [4] is a fast CBC parameter estimation pipeline in Python. RapidPE-RIFT parallelizes parameter estimation by fixing the intrinsic parameters (such as the masses and spins of the binary) to a grid around a search-identified intrinsic point and by integrating over the extrinsic parameters (such as sky location, distance, etc) via Monte Carlo sampling. For all events, there is an automated RapidPE-RIFT analysis that explores the masses holding the spins fixed to the search identified values. The analysis is accelerated using a variety of tricks and completes within a few minutes.

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 [10]. The cWB sky localization is included in the preliminary alert.

Refined sky localizations for unmodeled bursts are provided by two algorithms that, like Bilby, use MCMC and nested sampling methodologies. LALInference Burst (LIB) [11] models the signal as a single sinusoidally modulated Gaussian. BayesWave [12] 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.