Bayesian nonparametric spectral density estimation using B-spline 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 B-spline 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 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 $L_1$-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.

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Cited by in corpus (12)

• Parameter estimation with gravitational waves
• Cover Your Basis: Comprehensive Data-Driven Characterization of the Binary Black Hole Population
• Uncovering gravitational-wave backgrounds from noises of unknown shape with LISA
• Bayesian nonparametric spectral density estimation using B-spline priors
• Identifying and Addressing Nonstationary LISA Noise
• Computational Techniques for Parameter Estimation of Gravitational Wave Signals
• Bayesian spectral density estimation using P-splines with quantile-based knot placement
• Spectral Subsampling MCMC for Stationary Time Series
• Beyond Whittle: Nonparametric correction of a parametric likelihood with a focus on Bayesian time series analysis
• A nonparametrically corrected likelihood for Bayesian spectral analysis of multivariate time series
• Posterior consistency for the spectral density of non-Gaussian stationary time series
• Optimally adaptive Bayesian spectral density estimation for stationary and nonstationary processes