# Parameter estimation of compact binaries

The estimation of parameter values and associated waveforms of observed compact-binary coalescences (CBCs) is an important contribution to the science case of GW detectors. It is key to tests of general relativity, to many cosmological studies, to population studies of compact objects, to studies of gravitational lensing of gravitational waves, and of course, to the exploration of the nature and properties of the objects involved in the merger.

One of the libraries used for CBC parameter estimation is Bilby [Ashton et al (2019)]. It is written in Python, and its main function is to provide tools for Bayesian inference. It uses the waveform models defined in the LALSimulation package [LALSimulation]. We have used Bilby for the simulation of third-generation detector networks and parameter estimation by posterior sampling for the investigation of a CBC foreground reduction as described in the Cosmology page.

Another popular analysis framework is based on Fisher matrices, which can be used to calculate Gaussian estimation errors, i.e., it is based on an approximation of the likelihood function as a Gaussian distribution. The advantage is significantly faster computations compared to posterior or likelihood sampling. This framework was developed in a time-domain simulation of GW data for future detector networks to investigate their capabilities to estimate intrinsic and extrinsic source parameters focusing on the multi-band observation with detectors sensitive in different frequencies, e.g., combining data from space-borne and ground-based detectors [Grimm / Harms (2020)].

The Fisher-matrix software was also used to provide source-localization errors with Einstein Telescope (alone or together with detectors hosted by the already existing infrastructures), where the day-long observation time of neutron-star binaries with Einstein Telescope means that modulations of the signal due to Earth rotation can be observed, which greatly reduces sky-localization errors. This work was included in a paper on the Einstein Telescope science case [Maggiore et al (2020)].