BayesWave: Bayesian inference for gravitational wave bursts and instrument glitches. A central challenge in gravitational wave astronomy is identifying weak signals in the presence of non-stationary and non-Gaussian noise. The separation of gravitational wave signals from noise requires good models for both. When accurate signal models are available, such as for binary Neutron star systems, it is possible to make robust detection statements even when the noise is poorly understood. In contrast, searches for ’un-modeled’ transient signals are strongly impacted by the methods used to characterize the noise. Here we take a Bayesian approach and introduce a multi-component, variable dimension, parameterized noise model that explicitly accounts for non-stationarity and non-Gaussianity in data from interferometric gravitational wave detectors. Instrumental transients (glitches) and burst sources of gravitational waves are modeled using a Morlet–Gabor continuous wavelet frame. The number and placement of the wavelets is determined by a trans-dimensional reversible jump Markov chain Monte Carlo algorithm. The Gaussian component of the noise and sharp line features in the noise spectrum are modeled using the BayesLine algorithm, which operates in concert with the wavelet model.