arXiv subjects

Renate Meyer

Publications and source records attributed to Renate Meyer.

At least 37 records · Page 2Linked to original sources

arXiv2022

Ability of LISA to detect a gravitational-wave background of cosmological origin: the cosmic string case

We investigate the ability of the Laser Interferometer Space Antenna (LISA) to detect a stochastic gravitational-wave background (GWB) produced by cosmic strings, and to subsequently estimate the string tension $Gμ$ in the presence of instrument noise, an astrophysical background from compact binaries, and the galactic foreground from white dwarf binaries. Fisher Information and Markov Chain Monte Carlo methods provide estimates of the LISA noise and the parameters for the different signal sources. We demonstrate the ability of LISA to simultaneously estimate the galactic foreground, as well as the astrophysical and cosmic string produced backgrounds. Considering the expected astrophysical background and a galactic foreground, a cosmic string tension in the $G μ\approx 10^{-16}$ to $Gμ\approx 10^{-15}$ range or bigger could be measured by LISA, with the galactic foreground affecting this limit more than the astrophysical background. The parameter estimation methods presented here can be applied to other cosmological backgrounds in the LISA observation band.

gr-qc↗

arXiv2021

Inference of proto-neutron star properties from gravitational-wave data in core-collapse supernovae

The eventual detection of gravitational waves from core-collapse supernovae (CCSN) will help improve our current understanding of the explosion mechanism of massive stars. The stochastic nature of the late post-bounce gravitational wave signal due to the non-linear dynamics of the matter involved and the large number of degrees of freedom of the phenomenon make the source parameter inference problem very challenging. In this paper we take a step towards that goal and present a parameter estimation approach which is based on the gravitational waves associated with oscillations of proto-neutron stars (PNS). Numerical simulations of CCSN have shown that buoyancy-driven g-modes are responsible for a significant fraction of the gravitational wave signal and their time-frequency evolution is linked to the physical properties of the compact remnant through universal relations, as demonstrated in [1]. We use a set of 1D CCSN simulations to build a model that relates the evolution of the PNS properties with the frequency of the dominant g-mode, which is extracted from the gravitational-wave data using a new algorithm we have developed for our study. The model is used to infer the time evolution of a combination of the mass and the radius of the PNS. The performance of the method is estimated employing simulations of 2D CCSN waveforms covering a progenitor mass range between 11 and 40 solar masses and different equations of state. Considering signals embedded in Gaussian gravitational wave detector noise, we show that it is possible to infer PNS properties for a galactic source using Advanced LIGO and Advanced Virgo data at design sensitivities. Third generation detectors such as Einstein Telescope and Cosmic Explorer will allow to test distances of ${\cal O}(100\, {\rm kpc})$.

gr-qc↗

arXiv2021

Posterior consistency for the spectral density of non-Gaussian stationary time series

Various nonparametric approaches for Bayesian spectral density estimation of stationary time series have been suggested in the literature, mostly based on the Whittle likelihood approximation. A generalization of this approximation has been proposed in Kirch et al. who prove posterior consistency for spectral density estimation in combination with the Bernstein-Dirichlet process prior for Gaussian time series. In this paper, we will extend the posterior consistency result to non-Gaussian time series by employing a general consistency theorem of Shalizi for dependent data and misspecified models. As a special case, posterior consistency for the spectral density under the Whittle likelihood as proposed by Choudhuri, Ghosal and Roy is also extended to non-Gaussian time series. Small sample properties of this approach are illustrated with several examples of non-Gaussian time series.

math.ST↗

arXiv2021

Spectral separation of the stochastic gravitational-wave background for LISA in the context of a modulated Galactic foreground

Within its observational band the Laser Interferometer Space Antenna, LISA, will simultaneously observe orbital modulated waveforms from Galactic white dwarf binaries, a binary black hole produced gravitational-wave background, and potentially a cosmologically created stochastic gravitational-wave background (SGWB). The overwhelming majority of stars end their lives as white dwarfs, making them very numerous in the Milky Way. We simulate Galactic white dwarf binary gravitational-wave emission based on distributions from various mock catalogs and determine a complex waveform from the Galactic foreground with $3.5 \times 10^{7}$ binaries. We describe the effects from the Galactic binary distribution population across mass, position within the Galaxy, core type, and orbital frequency distribution. We generate the modulated Galactic white dwarf signal detected by \textit{LISA} due to its orbital motion, and present a data analysis strategy to address it. The Fisher Information and Markov Chain Monte Carlo methods give an estimation of the \textit{LISA} noise and the parameters for the different signal classes. We estimate the detectable limits for the future LISA observation of the SGWB in the spectral domain with the 3 \textit{LISA} channels $A$, $E$, and $T$. We simultaneously estimate the Galactic foreground, the astrophysical and cosmological backgrounds. Assuming the expected astrophysical background and a Galactic foreground, a cosmological background energy density of around $Ω_{GW,Cosmo} \approx 8 \times 10^{-13}$ could be detected by LISA. LISA will either detect a cosmologically produced SGWB, or set a limit that will have important consequences.

gr-qc↗

arXiv2021

Spectral separation of the stochastic gravitational-wave background for LISA: observing both cosmological and astrophysical backgrounds

With the goal of attempting to observe a stochastic gravitational wave background (SGWB) with LISA, the spectral separability of the cosmological and astrophysical backgrounds is important to estimate. We attempt to determine the level with which a cosmological background can be observed given the predicted astrophysical background level. We predict detectable limits for the future LISA measurement of the SGWB. Adaptive Markov chain Monte-Carlo methods are used to produce estimates with the simulated data from the LISA Data challenge (LDC). We also calculate the Cramer-Rao lower bound on the variance of the SGWB parameter uncertainties based on the inverse Fisher Information using the Whittle Likelihood. The estimation of the parameters is done with the 3 LISA channels $A$, $E$, and $T$. We simultaneously estimate the noise using a LISA noise model. Assuming the expected astrophysical background, a cosmological background energy density of around $Ω_{GW,Cosmo} \approx 1 \times 10^{-12}$ to $1 \times 10^{-13}$ can be detected by LISA.

gr-qc↗

arXiv2021

Spectral separation of the stochastic gravitational-wave background for LISA: galactic, cosmological and astrophysical backgrounds

In its observation band, the Laser Interferometer Space Antenna (LISA) will simultaneously observe stochastic gravitational-wave background (SGWB) signals of different origins; orbitally modulated waveforms from galactic white dwarf binaries, a binary black hole produced background, and possibly a cosmologically produced SGWB. We simulate the emission of gravitational waves from galactic white dwarf binaries based on the Lamberts \cite{Lamberts} distributions and determine a complex waveform from the galactic foreground. We generate the modulated galactic signal detected by LISA due to its orbital motion, and present a data analysis strategy to address it. The Fisher Information and Markov Chain Monte Carlo methods give an estimate of the LISA noise and parameters for the different signal sources. We simultaneously estimate the galactic foreground, the astrophysical and cosmological backgrounds, and estimate detection limits for the future LISA observation of the SGWB in the spectral domain with the 3 LISA channels $ A $, $ E $ and $ T $. In the context of the expected astrophysical background and a galactic foreground, a cosmological background energy density of about $ Ω_{GW,Cosmo} \approx 8 \times 10^{-13} $ could be detected by LISA with our spectral separation strategy.

gr-qc↗

arXiv2021

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

This article proposes a Bayesian approach to estimating the spectral density of a stationary time series using a prior based on a mixture of P-spline distributions. Our proposal is motivated by the B-spline Dirichlet process prior of Edwards et al. (2019) in combination with Whittle's likelihood and aims at reducing the high computational complexity of its posterior computations. The strength of the B-spline Dirichlet process prior over the Bernstein-Dirichlet process prior of Choudhuri et al. (2004) lies in its ability to estimate spectral densities with sharp peaks and abrupt changes due to the flexibility of B-splines with variable number and location of knots. Here, we suggest to use P-splines of Eilers and Marx (1996) that combine a B-spline basis with a discrete penalty on the basis coefficients. In addition to equidistant knots, a novel strategy for a more expedient placement of knots is proposed that makes use of the information provided by the periodogram about the steepness of the spectral power distribution. We demonstrate in a simulation study and two real case studies that this approach retains the flexibility of the B-splines, achieves similar ability to accurately estimate peaks due to the new data-driven knot allocation scheme but significantly reduces the computational costs.

stat.ME↗

arXiv2020

Computational Techniques for Parameter Estimation of Gravitational Wave Signals

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.

gr-qc↗

arXiv2020

Identifying and Addressing Nonstationary LISA Noise

We anticipate noise from the Laser Interferometer Space Antenna (LISA) will exhibit nonstationarities throughout the duration of its mission due to factors such as antenna repointing, cyclostationarities from spacecraft motion, and glitches as highlighted by LISA Pathfinder. In this paper, we use a surrogate data approach to test the stationarity of a time series which does not rely on the Gaussianity assumption. The main goal is to identify noise nonstationarities in the future LISA mission. This will be necessary for determining how often the LISA noise power spectral density (PSD) will need to be updated for parameter estimation routines. We conduct a thorough simulation study illustrating the power/size of various versions of the hypothesis tests, and then apply these approaches to differential acceleration measurements from LISA Pathfinder. We also develop a data analysis strategy for addressing nonstationarities in the LISA PSD, where we update the noise PSD over time, while simultaneously conducting parameter estimation, with a focus on planned data gaps.

gr-qc↗

arXiv2018

Bayesian Nonparametric Analysis of Multivariate Time Series: A Matrix Gamma Process Approach

While there is an increasing amount of literature about Bayesian time series analysis, only a few Bayesian nonparametric approaches to multivariate time series exist. Most methods rely on Whittle's Likelihood, involving the second order structure of a stationary time series by means of its spectral density matrix. This is often modeled in terms of the Cholesky decomposition to ensure positive definiteness. However, asymptotic properties such as posterior consistency or posterior contraction rates are not known. A different idea is to model the spectral density matrix by means of random measures. This is in line with existing approaches for the univariate case, where the normalized spectral density is modeled similar to a probability density, e.g. with a Dirichlet process mixture of Beta densities. In this work, we present a related approach for multivariate time series, with matrix-valued mixture weights induced by a Hermitian positive definite Gamma process. The proposed procedure is shown to perform well for both simulated and real data. Posterior consistency and contraction rates are also established.

stat.ME↗

arXiv2018

The stepping-stone sampling algorithm for calculating the evidence of gravitational wave models

Bayesian statistical inference has become increasingly important for the analysis of observations from the Advanced LIGO and Advanced Virgo gravitational-wave detectors. To this end, iterative simulation techniques, in particular nested sampling and parallel tempering, have been implemented in the software library LALInference to sample from the posterior distribution of waveform parameters of compact binary coalescence events. Nested sampling was mainly developed to calculate the marginal likelihood of a model but can produce posterior samples as a by-product. Thermodynamic integration is employed to calculate the evidence using samples generated by parallel tempering but has been found to be computationally demanding. Here we propose the stepping-stone sampling algorithm, originally proposed by Xie et al. (2011) in phylogenetics and a special case of path sampling, as an alternative to thermodynamic integration. The stepping-stone sampling algorithm is also based on samples from the power posteriors of parallel tempering but has superior performance as fewer temperature steps and thus computational resources are needed to achieve the same accuracy. We demonstrate its performance and computational costs in comparison to thermodynamic integration and nested sampling in a simulation study and a case study of computing the marginal likelihood of a binary black hole signal model applied to simulated data from the Advanced LIGO and Advanced Virgo gravitational wave detectors. To deal with the inadequate methods currently employed to estimate the standard errors of evidence estimates based on power posterior techniques, we propose a novel block bootstrap approach and show its potential in our simulation study and LIGO application.

physics.data-an↗

arXiv2018

Bayesian nonparametric spectral density estimation using B-spline priors

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.

stat.CO↗

arXiv2017

Beyond Whittle: Nonparametric correction of a parametric likelihood with a focus on Bayesian time series analysis

The Whittle likelihood is widely used for Bayesian nonparametric estimation of the spectral density of stationary time series. However, the loss of efficiency for non-Gaussian time series can be substantial. On the other hand, parametric methods are more powerful if the model is well-specified, but may fail entirely otherwise. Therefore, we suggest a nonparametric correction of a parametric likelihood taking advantage of the efficiency of parametric models while mitigating sensitivities through a nonparametric amendment. Using a Bernstein-Dirichlet prior for the nonparametric spectral correction, we show posterior consistency and illustrate the performance of our procedure in a simulation study and with LIGO gravitational wave data.

stat.ME↗

arXiv2015

Bayesian semiparametric power spectral density estimation with applications in gravitational wave data analysis

The standard noise model in gravitational wave (GW) data analysis assumes detector noise is stationary and Gaussian distributed, with a known power spectral density (PSD) that is usually estimated using clean off-source data. Real GW data often depart from these assumptions, and misspecified parametric models of the PSD could result in misleading inferences. We propose a Bayesian semiparametric approach to improve this. We use a nonparametric Bernstein polynomial prior on the PSD, with weights attained via a Dirichlet process distribution, and update this using the Whittle likelihood. Posterior samples are obtained using a blocked Metropolis-within-Gibbs sampler. We simultaneously estimate the reconstruction parameters of a rotating core collapse supernova GW burst that has been embedded in simulated Advanced LIGO noise. We also discuss an approach to deal with non-stationary data by breaking longer data streams into smaller and locally stationary components.

gr-qc↗

arXiv2014

Bayesian parameter estimation of core collapse supernovae using gravitational wave simulations

Using the latest numerical simulations of rotating stellar core collapse, we present a Bayesian framework to extract the physical information encoded in noisy gravitational wave signals. We fit Bayesian principal component regression models with known and unknown signal arrival times to reconstruct gravitational wave signals, and subsequently fit known astrophysical parameters on the posterior means of the principal component coefficients using a linear model. We predict the ratio of rotational kinetic energy to gravitational energy of the inner core at bounce by sampling from the posterior predictive distribution, and find that these predictions are generally very close to the true parameter values, with $90\%$ credible intervals $\sim 0.04$ and $\sim 0.06$ wide for the known and unknown arrival time models respectively. Two supervised machine learning methods are implemented to classify precollapse differential rotation, and we find that these methods discriminate rapidly rotating progenitors particularly well. We also introduce a constrained optimization approach to model selection to find an optimal number of principal components in the signal reconstruction step. Using this approach, we select 14 principal components as the most parsimonious model.

physics.data-an↗

arXiv2013

Bayesian inference on EMRI signals using low frequency approximations

Extreme mass ratio inspirals (EMRIs) are thought to be one of the most exciting gravitational wave sources to be detected with LISA. Due to their complicated nature and weak amplitudes the detection and parameter estimation of such sources is a challenging task. In this paper we present a statistical methodology based on Bayesian inference in which the estimation of parameters is carried out by advanced Markov chain Monte Carlo (MCMC) algorithms such as parallel tempering MCMC. We analysed high and medium mass EMRI systems that fall well inside the low frequency range of LISA. In the context of the Mock LISA Data Challenges, our investigation and results are also the first instance in which a fully Markovian algorithm is applied for EMRI searches. Results show that our algorithm worked well in recovering EMRI signals from different (simulated) LISA data sets having single and multiple EMRI sources and holds great promise for posterior computation under more realistic conditions. The search and estimation methods presented in this paper are general in their nature, and can be applied in any other scenario such as AdLIGO, AdVIRGO and Einstein Telescope with their respective response functions.

gr-qc↗

arXiv2010

Modelling coloured residual noise in gravitational-wave signal processing

We introduce a signal processing model for signals in non-white noise, where the exact noise spectrum is a priori unknown. The model is based on a Student's t distribution and constitutes a natural generalization of the widely used normal (Gaussian) model. This way, it allows for uncertainty in the noise spectrum, or more generally is also able to accommodate outliers (heavy-tailed noise) in the data. Examples are given pertaining to data from gravitational wave detectors.

stat.ME↗

arXiv2009

Bayesian reconstruction of gravitational wave burst signals from simulations of rotating stellar core collapse and bounce

Presented in this paper is a technique that we propose for extracting the physical parameters of a rotating stellar core collapse from the observation of the associated gravitational wave signal from the collapse and core bounce. Data from interferometric gravitational wave detectors can be used to provide information on the mass of the progenitor model, precollapse rotation and the nuclear equation of state. We use waveform libraries provided by the latest numerical simulations of rotating stellar core collapse models in general relativity, and from them create an orthogonal set of eigenvectors using principal component analysis. Bayesian inference techniques are then used to reconstruct the associated gravitational wave signal that is assumed to be detected by an interferometric detector. Posterior probability distribution functions are derived for the amplitudes of the principal component analysis eigenvectors, and the pulse arrival time. We show how the reconstructed signal and the principal component analysis eigenvector amplitude estimates may provide information on the physical parameters associated with the core collapse event.

gr-qc↗