Beyond Whittle: Nonparametric correction of a parametric likelihood with a focus on Bayesian time series analysis
  The Whittle likelihood is widely used for Bayesian nonparametric estimation
of the spectral density of stationary time series. However, the loss of
efficiency for non-Gaussian time series can be substantial. On the other hand,
parametric methods are more powerful if the model is well-specified, but may
fail entirely otherwise. Therefore, we suggest a nonparametric correction of a
parametric likelihood taking advantage of the efficiency of parametric models
while mitigating sensitivities through a nonparametric amendment. Using a
Bernstein-Dirichlet prior for the nonparametric spectral correction, we show
posterior consistency and illustrate the performance of our procedure in a
simulation study and with LIGO gravitational wave data.
