  The standard noise model in gravitational wave (GW) data analysis assumes
detector noise is stationary and Gaussian distributed, with a known power
spectral density (PSD) that is usually estimated using clean off-source data.
Real GW data often depart from these assumptions, and misspecified parametric
models of the PSD could result in misleading inferences. We propose a Bayesian
semiparametric approach to improve this. We use a nonparametric Bernstein
polynomial prior on the PSD, with weights attained via a Dirichlet process
distribution, and update this using the Whittle likelihood. Posterior samples
are obtained using a blocked Metropolis-within-Gibbs sampler. We simultaneously
estimate the reconstruction parameters of a rotating core collapse supernova GW
burst that has been embedded in simulated Advanced LIGO noise. We also discuss
an approach to deal with non-stationary data by breaking longer data streams
into smaller and locally stationary components.
