We present a new Bayesian nonparametric approach to estimating the spectraldensity of a stationary time series. A nonparametric prior based on a mixtureof B-spline distributions is specified and can be regarded as a generalizationof the Bernstein polynomial prior of Petrone (1999a,b) and Choudhuri et al.(2004). Whittle's likelihood approximation is used to obtain thepseudo-posterior distribution. This method allows for a data-driven choice ofthe smoothing parameter as well as the number and the location of the knots.Posterior samples are obtained using a parallel temperedMetropolis-within-Gibbs Markov chain Monte Carlo algorithm. We conduct asimulation study to demonstrate that for complicated spectral densities, theB-spline prior provides more accurate Monte Carlo estimates in terms of$L_1$-error and uniform coverage probabilities than the Bernstein polynomialprior. Finally, we demonstrate the algorithm's ability to estimate a spectraldensity with sharp features, using real gravitational wave detector data fromLIGO's sixth science run.
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