Bayesian spectral density estimation using P-splines with quantile-based knot placement

Maturana-Russel, Patricio; Meyer, Renate

doi:10.1007/s00180-021-01066-7

Cited by 7 publications

(2 citation statements)

References 32 publications

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“…An MCMC algorithm combined with parallel tempering was used for posterior computation. A recent modification that reduces the computational complexity while keeping the good approximation and coverage properties of the B‐splines by using P‐splines, that is, B‐splines but with fixed knots and a smoothness penalty on the coefficients, is given in Maturana‐Russel and Meyer (2019) and implemented in the R package psplinePsd (Maturana‐Russel & Meyer, 2020). By taking advantage of a well‐fitting parametric autoregressive model, Kirch et al (2019) can improve on the Whittle likelihood approximation using a nonparametric correction of a parametric working model and prove posterior consistency.…”

Section: Interferometer Noisementioning

confidence: 99%

Computational techniques for parameter estimation of gravitational wave signals

Meyer

Edwards

Maturana-Russel

et al. 2020

WIREs Computational Stats

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Since the very first detection of gravitational waves from the coalescence of two black holes in 2015, Bayesian statistical methods have been routinely applied by LIGO and Virgo to extract the signal out of noisy interferometric measurements, obtain point estimates of the physical parameters responsible for producing the signal, and rigorously quantify their uncertainties. Different computational techniques have been devised depending on the source of the gravitational radiation and the gravitational waveform model used. Prominent sources of gravitational waves are binary black hole or neutron star mergers, the only objects that have been observed by detectors to date. But also gravitational waves from core collapse supernovae, rapidly rotating neutron stars, and the stochastic gravitational wave background are in the sensitivity band of the ground-based interferometers and expected to be observable in future observation runs. As nonlinearities of the complex waveforms and the high-dimensional parameter spaces preclude analytic evaluation of the posterior distribution, posterior inference for all these sources relies on computer-intensive simulation techniques such as Markov chain Monte Carlo methods. A review of state-of-the-art Bayesian statistical parameter estimation methods will be given for researchers in this cross-disciplinary area of gravitational wave data analysis.

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Section: Interferometer Noisementioning

confidence: 99%

Computational techniques for parameter estimation of gravitational wave signals

Meyer

Edwards

Maturana-Russel

et al. 2020

WIREs Computational Stats

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“…For example, Pawitan and O'Sullivan (1994) estimated the spectral density from a penalized Whittle likelihood, while Kooperberg et al (1995) used polynomial splines to estimate the log-spectral density function maximizing the Whittle likelihood. Recently, Bayesian methods for spectral density estimation have been proposed (see Choudhuri et al, 2004;Edwards et al, 2019;Maturana-Russel and Meyer, 2021), but these may become very computationally intensive in large samples due to posterior sampling.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Block-Toeplitz Covariance Matrices

Fuhrmann¹,

Barton²

1990 Conference Record Twenty-Fourth Asilomar Conference on Signals, Systems and Computers, 1990.

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We consider the problem of estimating structured covarimws using maximum-likelihood methodology. The structured covariance matrices of interest here are block-Toeplitz matrices and Toeplitz-block-Toeplitz matrices. These arise naturally in wideband array processing, and in narrowband array processing with rectangular arrays. An EM algorithm for estimating a blockToeplitz matrix is derived based on an embedding in a larger block-circulant matrix. An EM algorithm for estimating a Toeplitz-block-Toeplitz matrix is derived based on an embedding in a larger circulant-blockcidant matrix.

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