期刊
STATISTICS AND COMPUTING
卷 29, 期 1, 页码 67-78出版社
SPRINGER
DOI: 10.1007/s11222-017-9796-9
关键词
B-spline prior; Bernstein polynomial prior; Whittle likelihood; Spectral density estimation; Bayesian nonparametrics; LIGO; Gravitational waves; Sunspot cycle
资金
- National Science Foundation [PHY-1505373]
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 B-spline distributions is specified and can be regarded as a generalization of the Bernstein polynomial prior of Petrone (Scand J Stat 26:373-393, 1999a; Can J Stat 27:105-126, 1999b) and Choudhuri et al. (J Am Stat Assoc 99(468):1050-1059, 2004). Whittle's likelihood approximation is used to obtain the pseudo-posterior distribution. This method allows for a data-driven choice of the number of mixture components and the location of knots. Posterior samples are obtained using a Metropolis-within-Gibbs 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 B-spline prior provides more accurate Monte Carlo estimates in terms of L1-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.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据