# 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.

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