  This review provides a conceptual and technical survey of methods for
parameter estimation of gravitational wave signals in ground-based
interferometers such as LIGO and Virgo. We introduce the framework of Bayesian
inference and provide an overview of models for the generation and detection of
gravitational waves from compact binary mergers, focusing on the essential
features that are observable in the signals. Within the traditional
likelihood-based paradigm, we describe various approaches for enhancing the
efficiency and robustness of parameter inference. This includes techniques for
accelerating likelihood evaluations, such as heterodyne/relative binning,
reduced-order quadrature, multibanding and interpolation. We also cover methods
to simplify the analysis to improve convergence, via reparametrization,
importance sampling and marginalization. We end with a discussion of recent
developments in the application of likelihood-free (simulation-based) inference
methods to gravitational wave data analysis.
