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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 Bayes factor to assess evidence. We introduce generalized steppingstone (GSS) as an efficient and accurate marginal likelihood estimation method for the PTA-Bayesian framework. This method enables cheaper 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., Comment: 8 pages, 5 figures, submitted to MNRAS

Core-Collapse Supernovae (CCSNe) remain a critical focus in the search for gravitational waves (GWs) in modern astronomy. Their detection and subsequent analysis will enhance our understanding of the explosion mechanisms in massive stars. This paper investigates a combination of time-frequency analysis tools with convolutional neural network (CNN) to enhance the detection of GWs originating from CCSNe. The CNN was trained in the time-frequency domain using simulated data from Advanced LIGO (aLIGO). We preprocess the data using the widely used Short-Time Fourier Transform (STFT) and the Q-transform. Our CNN model achieves a remarkable 100% prediction rate for CCSNe GW events with a Signal-to-Noise Ratio (SNR) greater than 0.5. We found that the STFT outperforms the Q-transform for SNRs below 0.5., Comment: 7 pages, 12 figures, submitted to Expert Systems with Applications

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.

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 ${\cal O}(100\, {\rm kpc})$.

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., Comment: 45 pages, 5 figures, to be published in Wiley Interdisciplinary Reviews -- Computational Statistics

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., Comment: 19 pages, 17 figures

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., Comment: 5 figures, 4 tables