Bayesian nonparametric spectral density estimation using Bspline priors
Abstract
We present a new Bayesian nonparametric approach to estimating the spectral density of a stationary time series. A nonparametric prior based on a mixture of Bspline distributions is specified and can be regarded as a generalization of the Bernstein polynomial prior of Petrone (1999a,b) and Choudhuri et al. (2004). Whittle's likelihood approximation is used to obtain the pseudoposterior distribution. This method allows for a datadriven choice of the number of mixture components and the location of knots. Posterior samples are obtained using a MetropoliswithinGibbs Markov chain Monte Carlo algorithm, and mixing is improved using parallel tempering. We conduct a simulation study to demonstrate that for complicated spectral densities, the Bspline prior provides more accurate Monte Carlo estimates in terms of $L_1$error and uniform coverage probabilities than the Bernstein polynomial prior. We apply the algorithm to annual mean sunspot data to estimate the solar cycle. Finally, we demonstrate the algorithm's ability to estimate a spectral density with sharp features, using real gravitational wave detector data from LIGO's sixth science run, recoloured to match the Advanced LIGO target sensitivity.
 Publication:

arXiv eprints
 Pub Date:
 July 2017
 arXiv:
 arXiv:1707.04878
 Bibcode:
 2017arXiv170704878E
 Keywords:

 Statistics  Computation
 EPrint:
 Edwards, M.C., Meyer, R. &