arXiv subjects

Renate Meyer

Publications and source records attributed to Renate Meyer.

At least 19 recordsLinked to original sources

arXiv2026

Variational Bayesian Inference for the Spectral Structure of LISA Noise

Estimating spectral density matrices for future space-based gravitational-wave detectors such as LISA is challenging due to the long duration of the data and the correlated instrumental noise across multiple time-delay interferometry channels. In this work, we investigate a specialized mean-field stochastic gradient variational Bayes (SGVB) procedure for fast posterior approximation in long-duration multivariate spectral density estimation. Based on the existing eigenbasis representation of the blocked Whittle likelihood approach, the posterior model applies a Cholesky factorization to represent the inverse spectral density matrix and models the resulting frequency-dependent entries with cosine basis functions, with a discounted regularized horseshoe prior assigned to the basis coefficients. We test mean-field SGVB as a stand-alone posterior approximation by comparing it with Hamiltonian Monte Carlo (HMC) targeting the same posterior model. In simulation studies based on autoregressive and moving average processes, SGVB produces posterior median spectral estimates close to those obtained from HMC at substantially lower computational cost. We then apply the method to two one-year, fixed-delay, stationary, noise-only LISA simulations and show that the SGVB spectral density estimates are consistent with HMC and Welch estimates across the LISA analysis band, while requiring substantially less computation. These results demonstrate that SGVB provides a scalable Bayesian approach to spectral density estimation for long-duration multivariate LISA noise analysis.

astro-ph.IM↗

arXiv2026

Bayesian P-spline recovery of stochastic gravitational-wave backgrounds in LISA

The detection of a stochastic gravitational-wave background (SGWB) is a primary science objective for the Laser Interferometer Space Antenna (LISA). However, extracting these signals is difficult because both the signal and the instrumental noise are stochastic and overlapping in the millihertz band. In this work, we present a Bayesian framework for the joint estimation of LISA noise and SGWB signals. Our approach models the LISA instrumental noise using flexible log-penalized splines, employing a roughness penalty to prevent overfitting while maintaining computational efficiency. For the SGWB, we compare a power-law model with a spline-based model and study how the choice of signal model and noise prior affects signal recovery and detection. Using simulated LISA data, we find that the power-law model gives tighter estimates when the signal follows the assumed shape. However, it fails to recover a localized spectral feature that is not described by a power law, causing the signal to be absorbed by the instrumental-noise spline. The fully spline-based model is less restrictive and successfully recovers such features. We also find that stronger prior information about the test-mass noise helps reduce the degeneracy between the noise and SGWB models at low frequencies, improving signal detection. These results reflect a single trade-off: added model flexibility reduces sensitivity when the assumed signal shape is correct, and prevents bias when it is not.

gr-qc↗

arXiv2026

Insights into the Pulsar Timing Array hypothesis space

We present novel insights into the pulsar-noise model space in pulsar timing array (PTA) experiments. Through a comparative analysis of the same Parkes PTA second data release observations processed with the 2020 and 2023 pipelines, we show that data processing materially changes the distribution of posterior support across competing noise hypotheses and increases sensitivity to weak contributions such as the solar wind. A solar-wind component appears in the highest-posterior hypothesis for ten pulsars under the 2023 pipeline, against four under the 2020 pipeline, while the corresponding mean electron density estimates are consistent with PPTA DR3 results. Furthermore, hypothesis-space analysis exposes model competition and degeneracies that are hidden by single-model summaries. Approximately 75% of the pulsars retain substantial posterior support for alternative noise descriptions. Therefore, understanding the nature of the pulsar noise hypothesis space is crucial for robust inference and nanohertz gravitational-wave background searches.

astro-ph.HE↗

arXiv2026

Bayesian nonparametric estimation of correlated gravitational wave detector network noise using matrix-gamma process priors

This paper addresses the important problem of estimating the noise spectral density of next-generation gravitational-wave detectors, such as LISA and the Einstein Telescope (ET), where cross-channel correlations must be accounted for to avoid biased parameter estimation of gravitational-wave signals. Unlike approaches that estimate test-mass and optical-metrology-system noise separately at the single-link level and then map them to the Time-Delay Interferometry (TDI) channels through known transfer functions, we develop a Bayesian nonparametric method that directly estimates the spectral density matrix of the XYZ channels, thereby accommodating additional sources of uncertainty. Our approach combines a flexible matrix-gamma process prior on the matrix-valued coefficients of a Bernstein polynomial basis expansion with a blocked multivariate Whittle likelihood. The prior guarantees Hermitian positive definiteness of the spectral estimate at every frequency. To avoid reversible-jump methods, we use an adaptive Markov chain Monte Carlo (MCMC) algorithm for posterior sampling. The proposed framework can also be used to correct misspecified parametric noise models. Results from a simulation study and simulated correlated-noise data for both LISA and ET demonstrate the effectiveness of the proposed method.

gr-qc↗

arXiv2026

Multivariate Bayesian P-spline estimation of spectral density matrices, with application to LISA TDI noise

We present a Bayesian P-spline method for estimating the frequency-dependent cross-spectral density matrix of stationary multivariate time series. The inverse spectral matrix is parametrised through its frequency-varying Cholesky decomposition, which guarantees Hermitian positive definiteness at every frequency. Each real log-diagonal entry and each real and imaginary off-diagonal entry is given an independent penalised B-spline prior that controls smoothness. Inference uses a blocked, coarse-grained Whittle likelihood with safe-Bayes $\eta$-tempering to stabilise posterior calibration, sampled by the No-U-Turn Sampler from a variational initialisation. On synthetic VAR(2) benchmarks with known ground truth, the method recovers both diagonal and cross-spectral structure, attains near-nominal credible-interval coverage, and achieves a relative integrated squared (Frobenius) error (RISE) that decreases with sample size. We then apply the method to publicly released simulated LISA time-delay interferometry (TDI) data in two noise configurations. In the idealised symmetric case, the full multivariate model and a reduced model that assumes a diagonal AET noise covariance agree to within $\sim10^{-3}$ in RISE. Under realistic noise that is asymmetric across the six Movable Optical Sub-Assemblies (MOSAs), the AET-diagonal assumption fails by more than an order of magnitude in RISE ($\sim\!3.3\!\times\!10^{-2}$ versus $\sim\!10^{-3}$), whereas the full multivariate model recovers the cross-spectral structure.

stat.ME↗

arXiv2025

Enhancing evidence estimation through informed probability density approximation

We introduce the Morph approximation, a class of product approximations of probability densities that selects low-order disjoint parameter blocks by maximizing the sum of their total correlations. We use the posterior approximation via Morph as the importance distribution in optimal bridge sampling. We denote this procedure by MorphZ, which serves as a post-processing estimator of the marginal likelihood. The MorphZ estimator requires only posterior samples, and is fully agnostic regarding the choice of sampler. We evaluate MorphZ's performance across statistical benchmarks, pulsar timing array (PTA) models, compact binary coalescence (CBC) gravitational-wave (GW) simulations and the GW150914 event. Across these applications, spanning low to high dimensionalities, MorphZ yields accurate evidence estimates at substantially reduced computational cost relative to standard approaches. We have found that when these approaches fail to provide accurate estimates, MorphZ has proven to either resolve the estimation failure or significantly improve the results. Its bridge sampling relative error diagnostic provides conservative uncertainty estimates. Because MorphZ operates directly on posterior draws, it complements exploration-oriented samplers by enabling fast and reliable evidence estimation, while it can be seamlessly integrated into existing inference workflows.

astro-ph.IM↗

arXiv2025

Bayesian power spectral density estimation for LISA noise based on penalized splines with a parametric boost

Flexible and accurate noise characterization is crucial for the precise estimation of gravitational-wave parameters. We introduce a Bayesian method for estimating the power spectral density (PSD) of long, stationary time series, explicitly tailored for LISA data analysis. Our approach models the PSD as the geometric mean of a parametric and a nonparametric component, combining the knowledge from parametric models with the flexibility to capture deviations from theoretical expectations. The nonparametric component is expressed by a mixture of penalized B-splines. Adaptive, data-driven knot placement, performed once at initialization, removes the need for reversible-jump Markov chain Monte Carlo, while hierarchical roughness-penalty priors prevent overfitting. Validation on simulated autoregressive AR(4) data demonstrates estimator consistency and shows that well-matched parametric components reduce the integrated absolute error compared to an uninformative baseline, requiring fewer spline knots to achieve comparable accuracy. Applied to one year of simulated LISA X-channel (univariate) noise, our method achieves relative integrated absolute errors of $\mathcal{O}(10^{-2})$, making it suitable for iterative analysis pipelines and multi-year mission data sets.

gr-qc↗

arXiv2025

Gravitational wave energy spectral density properties from BPASS Galactic binary population in the Milky Way galaxy

We analyse the energy spectral density properties of Gravitational waves from Galactic binary populations in the~\text{mHz} band targeted by the Laser Interferometer Space Antenna mission. Our analysis is based on combining BPASS with a Milky Way analogue galaxy from the Feedback In Realistic Environment (FIRE) simulations and the GWs these populations emit. Our investigation compares different functional forms of gravitational wave (GW) ESDs, namely the single power-law, broken power-law, and single-peak models, revealing disparities within and among Galactic binary populations. We estimate the ESDs for six different Galactic binary populations and the ESD of the total Galactic binary population for LISA. Employing a single power-law model, we predict a total Galactic binary GW signal amplitude $α$ = $2.0^{+0.2}_{-0.2} \times 10^{-8}$ and a slope $β$ = $-2.64 ^{+0.03}_{-0.04}$ and the ESD $\rm h^2 Ω_{GW}$ = $1.1 ^{+0.1}_{-0.1} \times 10^{-9}$ at 3~\text{mHz}. For the Galactic WDB binary GW signal $α= 1^{+0.02}_{-0.02} \times 10^{-10}$, $β= -1.56 ^{+0.03}_{-0.03}$ and $\rm h^2 Ω_{GW} = 18 ^{+1}_{-1} \times 10^{-12}$. Our analysis underscores the importance of accurate noise parameter estimation and highlights the complexities of modelling realistic observations, prompting future exploration into more flexible models.

astro-ph.GA↗

arXiv2025

Generalized Steppingstone Sampling: Efficient marginal likelihood estimation in gravitational wave analysis of Pulsar Timing Array data

Globally, Pulsar Timing Array (PTA) experiments have revealed evidence supporting an existing gravitational wave background (GWB) signal in the PTA data set. Apart from acquiring more observations, the sensitivity of PTA experiments can be increased by improving the accuracy of the noise modeling. In PTA data analysis, noise modeling is conducted primarily using Bayesian statistics, relying on the marginal likelihood and the Bayes factor to assess the evidence. We introduce generalized steppingstone (GSS) as an efficient and accurate marginal likelihood estimation method for the PTA-Bayesian framework. This method enables low-cost estimates with high accuracy, especially when comparing expensive models such as the Hellings-Downs (HD) model or the overlap reduction function model (ORF). We demonstrate the efficiency and the accuracy of GSS for model selection and evidence calculation by reevaluating the evidence of previous analyses from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 15 yr data set and the European PTA (EPTA) second data release. We find similar evidence for the GWB compared to the one reported by the NANOGrav 15-year data set. Compared to the evidence reported for the EPTA second data release, we find a substantial increase in evidence supporting GWB across all data sets.

astro-ph.IM↗

arXiv2024

Predicting gravitational wave signals from BPASS White Dwarf Binary and Black Hole Binary populations of a Milky Way-like galaxy model for LISA

Galactic white dwarf binaries (WDBs) and black hole binaries (BHBs) will be gravitational wave (GW) sources for LISA. Their detection will provide insights into binary evolution and the evolution of our Galaxy through cosmic history. Here, we make predictions of the expected WDB and BHB population within our Galaxy. We combine predictions of the compact remnant binary populations expected by stellar evolution by using the detailed Binary Population and Spectral Synthesis code (BPASS) with a Milky Way analogue galaxy model from the Feedback In Realistic Environment (FIRE) simulations. We use \textsc{PhenomA} and \textsc{LEGWORK} to simulate LISA observations. Both packages make similar predictions that on average four Galactic BHBs and 673 Galactic WDBs above the signal-to-noise ratio (SNR) threshold of 7 after a four-year mission. We compare these predictions to earlier results using the Binary Star Evolution (BSE) code with the same FIRE model galaxy. We find that BPASS predicts a few more LISA observable Galactic BHBs and a twentieth of the Galactic WDBs. The differences are due to the different physical assumptions that have gone into the binary evolution calculations. These results indicate that the expected population of compact binaries that LISA will detect depends very sensitively on the binary population synthesis models used and thus observations of the LISA population will provide tight constraints on our modelling of binary stars. Finally, from our synthetic populations we have created mock LISA signals that can be used to test and refine data processing methods of the eventual LISA observations.

astro-ph.GA↗

arXiv2024

Asymptotic considerations in a Bayesian linear model with nonparametrically modelled time series innovations

This paper considers a semiparametric approach within the general Bayesian linear model where the innovations consist of a stationary, mean zero Gaussian time series. While a parametric prior is specified for the linear model coefficients, the autocovariance structure of the time series is modeled nonparametrically using a Bernstein-Gamma process prior for the spectral density function, the Fourier transform of the autocovariance function. When updating this joint prior with Whittle's likelihood, a Bernstein-von-Mises result is established for the linear model coefficients showing the asymptotic equivalence of the corresponding estimators to those obtained from frequentist pseudo-maximum-likelihood estimation under the Whittle likelihood. Local asymptotic normality of the likelihood is shown, demonstrating that the marginal posterior distribution of the linear model coefficients shrinks at parametric rate towards the true value, and that the conditional posterior distribution of the spectral density contracts in the sup-norm, even in the case of a partially misspecified linear model.

math.ST↗

arXiv2024

Variational inference for correlated gravitational wave detector network noise

Gravitational wave detectors like the Einstein Telescope and LISA generate long multivariate time series, which pose significant challenges in spectral density estimation due to a number of overlapping signals as well as the presence of correlated noise. Addressing both issues is crucial for accurately interpreting the signals detected by these instruments. This paper presents an application of a variational inference spectral density estimation method specifically tailored for dealing with correlated noise in the data. It is flexible in that it does not rely on any specific parametric form for the multivariate spectral density. The method employs a blocked Whittle likelihood approximation for stationary time series and utilizes the Cholesky decomposition of the inverse spectral density matrix to ensure a positive definite estimator. A discounted regularized horseshoe prior is applied to the spline coefficients of each Cholesky factor, and the posterior distribution is computed using a stochastic gradient variational Bayes approach. This method is particularly effective in addressing correlated noise, a significant challenge in the analysis of multivariate data from co-located detectors. The method is demonstrated by analyzing 2000 seconds of simulated Einstein Telescope noise, which shows its ability to produce accurate spectral density estimates and quantify coherence between time series components. This makes it a powerful tool for analyzing correlated noise in gravitational wave data.

gr-qc↗

arXiv2024

Calibrating approximate Bayesian credible intervals of gravitational-wave parameters

Approximations are commonly employed in realistic applications of scientific Bayesian inference, often due to convenience if not necessity. In the field of gravitational-wave (GW) data analysis, fast-to-evaluate but approximate waveform models of astrophysical GW signals are sometimes used in lieu of more accurate models to infer properties of a true GW signal buried within detector noise. In addition, a Fisher-information-based normal approximation to the posterior distribution can also be used to conduct inference in bulk, without the need for extensive numerical calculations such as Markov chain Monte Carlo (MCMC) simulations. Such approximations can generally lead to an inaccurate posterior distribution with poor statistical coverage of the true posterior. In this article, we present a novel calibration procedure that calibrates the credible sets for a family of approximate posterior distributions, to ensure coverage of the true posterior at a level specified by the analyst. Tools such as autoencoders and artificial neural networks are used within our calibration model to compress the data (for efficiency) and to perform tasks such as logistic regression. As a proof of principle, we demonstrate our formalism on the GW signal from a high-mass binary black hole merger, a promising source for the near-future space-based GW observatory LISA.

gr-qc↗

arXiv2023

A nonparametrically corrected likelihood for Bayesian spectral analysis of multivariate time series

This paper presents a novel approach to Bayesian nonparametric spectral analysis of stationary multivariate time series. Starting with a parametric vector-autoregressive model, the parametric likelihood is nonparametrically adjusted in the frequency domain to account for potential deviations from parametric assumptions. We show mutual contiguity of the nonparametrically corrected likelihood, the multivariate Whittle likelihood approximation and the exact likelihood for Gaussian time series. A multivariate extension of the nonparametric Bernstein-Dirichlet process prior for univariate spectral densities to the space of Hermitian positive definite spectral density matrices is specified directly on the correction matrices. An infinite series representation of this prior is then used to develop a Markov chain Monte Carlo algorithm to sample from the posterior distribution. The code is made publicly available for ease of use and reproducibility. With this novel approach we provide a generalization of the multivariate Whittle-likelihood-based method of Meier et al. (2020) as well as an extension of the nonparametrically corrected likelihood for univariate stationary time series of Kirch et al. (2019) to the multivariate case. We demonstrate that the nonparametrically corrected likelihood combines the efficiencies of a parametric with the robustness of a nonparametric model. Its numerical accuracy is illustrated in a comprehensive simulation study. We illustrate its practical advantages by a spectral analysis of two environmental time series data sets: a bivariate time series of the Southern Oscillation Index and fish recruitment and time series of windspeed data at six locations in California.

stat.ME↗

arXiv2023

Bayesian nonparametric spectral analysis of locally stationary processes

Based on a novel dynamic Whittle likelihood approximation for locally stationary processes, a Bayesian nonparametric approach to estimating the time-varying spectral density is proposed. This dynamic frequency-domain based likelihood approximation is able to depict the time-frequency evolution of the process by utilizing the moving periodogram previously introduced in the bootstrap literature. The posterior distribution is obtained by updating a bivariate extension of the Bernstein-Dirichlet process prior with the dynamic Whittle likelihood. Asymptotic properties such as sup-norm posterior consistency and L2-norm posterior contraction rates are presented. Additionally, this methodology enables model selection between stationarity and non-stationarity based on the Bayes factor. The finite-sample performance of the method is investigated in simulation studies and applications to real-life data-sets are presented.

stat.ME↗

arXiv2023

Prospects for LISA to detect a gravitational-wave background from first order phase transitions

First order phase transitions in the early universe could produce a gravitational-wave background that might be detectable by the Laser Interferometer Space Antenna (LISA). Such an observation would provide evidence for physics beyond the Standard Model. We study the ability of LISA to observe a gravitational-wave background from phase transitions in the presence of an extragalactic foreground from binary black hole mergers throughout the universe, a galactic foreground from white dwarf binaries, and LISA noise. Modelling the phase transition gravitational wave background as a double broken power law, we use the deviance information criterion as a detection statistic, and Fisher matrix and Markov Chain Monte Carlo methods to assess the measurement accuracy of the parameters of the power spectrum. While estimating all the parameters associated with the gravitational-wave backgrounds, foregrounds, and LISA noise, we find that LISA could detect a gravitational-wave background from phase transitions with a peak frequency of 1 mHz and normalized energy density amplitude of $Ω_{\text p} \simeq 3 \times 10^{-11}$. With $Ω_{\text p} \simeq 10^{-10}$, the signal is detectable if the peak frequency is in the range $4 \times 10^{-4}$ to $9 \times 10^{-3}$ Hz, and the peak amplitude and frequency can be estimated to an accuracy of 10\% to 1\%.

gr-qc↗

arXiv2022

Figures of merit for a stochastic gravitational-wave background measurement by LISA: implications of LISA Pathfinder noise correlations

An important goal of the Laser Interferometer Space Antenna (LISA) is to observe a stochastic gravitational-wave background (SGWB). A study of possible correlated noise in LISA is relevant to establish limits for this future measurement. To test noise investigation methods under somewhat realistic conditions, we use the data of LISA Pathfinder (LPF). We calculate the coherence between the LPF differential acceleration of the two test-masses with magnetic fields, temperature, and micronewton cold gas thruster activity in the spacecraft. We apply our observed correlations to LISA, and estimate how the presence of such correlated noise would affect its search for a SGWB. In the context of a figure of merit, we estimate the effect of noise on the LISA SGWB search.

gr-qc↗

arXiv2022

Parameter estimation with gravitational waves

The new era of gravitational wave astronomy truly began on September 14, 2015 with the detection of GW150914, the sensational first direct observation of gravitational waves from the inspiral and merger of two black holes by the two Advanced LIGO detectors. In the subsequent first three observing runs of the LIGO/Virgo network, gravitational waves from $\sim 50$ compact binary mergers have been announced, with more results to come. The events have mostly been produced by binary black holes, but two binary neutron star mergers have so far been observed, as well as the mergers of two neutron star - black hole systems. Furthermore, gravitational waves emitted by core-collapse supernovae, pulsars and the stochastic gravitational wave background are within the LIGO/Virgo/KAGRA sensitivity band and are likely to be observed in future observation runs. Beyond signal detection, a major challenge has been the development of statistical and computational methodology for estimating the physical waveform parameters and quantifying their uncertainties in order to accurately characterise the emitting system. These methods depend on the sources of the gravitational waves and the gravitational waveform model that is used. This article reviews the main waveform models and parameter estimation methods used to extract physical parameters from gravitational wave signals detected to date by LIGO and Virgo and from those expected to be observed in the future, which will include KAGRA, and how these methods interface with various aspects of LIGO/Virgo/KAGRA science. Also presented are the statistical methods used by LIGO and Virgo to estimate detector noise, test general relativity, and draw conclusions about the rates of compact binary mergers in the universe. Furthermore, a summary of major publicly available gravitational wave parameter estimation software packages is given.

gr-qc↗