arXiv subjects

Avi Vajpeyi

Publications and source records attributed to Avi Vajpeyi.

17 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

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

An explicit and differentiable Wilson-Daubechies-Meyer transform for gravitational-wave data analysis

The Wilson-Daubechies-Meyer (WDM) time-frequency transform has been widely used in gravitational-wave astronomy, yet a self-contained, mathematically explicit reference for practitioners remains lacking. This is especially true for those wishing to adopt the transform in modern Python and JAX inference workflows. We present wdm_transform, an open-source Python package implementing the WDM wavelet-packet time-frequency transform, and document its mathematical foundations, statistical properties, and practical implementation for gravitational-wave data analysis. The package supplies NumPy and JAX backends, both transforms (forward and inverse) validated to floating-point precision, with the JAX backend enabling GPU-accelerated transforms of million-point data streams in tens of milliseconds. As a worked example, we verify that the WDM-domain likelihood reproduces frequency-domain posteriors for a resolved LISA galactic binary under a shared stationary noise model, confirming numerical equivalence of the two representations in that controlled setting. This work paves the way for systematic optimisation of WDM tilings, a particularly promising direction for the non-stationary noise, stochastic backgrounds, and data gaps anticipated in future detectors, and for direct comparisons with alternative time-frequency representations needed to meet the challenges of future gravitational-wave data analysis.

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 $η$-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↗

arXiv2026

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↗

arXiv2026

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↗

arXiv2026

First-time assessment of glitch-induced bias and uncertainty in inference of extreme mass ratio inspirals

This work investigates the impact of streams of transient, non-Gaussian noise artifacts or "glitches" on the parameter estimation of extreme mass ratio inspirals (EMRI) in the Laser Interferometer Space Antenna (LISA). Glitches cause biased and less precise inference for short-duration signals such as massive black hole binaries, but their effect on long-lived sources such as EMRIs has not been quantified. Using simulated LISA observations containing injected EMRIs and streams of shapelet-based glitches drawn from the LISA Pathfinder catalog, we estimate the glitch-induced parameter biases and uncertainties through a Fisher-matrix-based analysis whose accuracy we verify with Markov-Chain Monte Carlo. We find that moderately mitigated glitch streams i.e. ones containing only glitches of up to moderate SNRs ($ρ\lesssim 90$) induce negligible to minor biases $[\sim0.04σ,\sim0.6σ]$ in the inferred EMRI parameters. In contrast, weakly mitigated glitch streams containing higher-SNR events ($ρ\lesssim 400$) can produce biases nearing $1σ$. These results demonstrate that, when compared to inference of other sources such as massive black hole binaries, EMRI inference is notably more robust to glitches. We stress that at least some amount of glitch modeling and mitigation remains essential for unbiased EMRI analyses in the LISA era.

gr-qc↗

arXiv2026

Analysis of GWTC-3 with fully precessing numerical relativity surrogate models

The third Gravitational-Wave Transient Catalog (GWTC-3) contains 90 binary coalescence candidates detected by the LIGO-Virgo-KAGRA Collaboration (LVK). We provide a re-analysis of binary black hole (BBH) events using a recently developed numerical relativity (NR) waveform surrogate model, NRSur7dq4, that includes all $\ell \leq 4$ spin-weighted spherical harmonic modes as well as the complete physical effects of precession. Properties of the remnant black holes' (BH's) mass, spin vector, and kick vector are found using an associated remnant surrogate model NRSur7dq4Remnant. Both NRSur7dq4 and NRSur7dq4Remnant models have errors comparable to numerical relativity simulations and allow for high-accuracy parameter estimates. We restrict our analysis to 47 BBH events that fall within the regime of validity of NRSur7dq4 (mass ratios greater than 1/6 and total masses greater than $60 M_{\odot}$). While for most of these events our results match the LVK analyses that were obtained using the semi-analytical models such as IMRPhenomXPHM and SEOBNRv4PHM, we find that for more than 20\% of events the NRSur7dq4 model recovers noticeably different measurements of black hole properties like the masses and spins, as well as extrinsic properties like the binary inclination and distance. For instance, GW150914_095045 exhibits noticeable differences in spin precession and spin magnitude measurements. Other notable findings include one event (GW191109_010717) that constrains the effective spin $χ_{eff}$ to be negative at a 99.3\% credible level and two events (GW191109_010717 and GW200129_065458) with well-constrained kick velocities. Furthermore, compared to the models used in the LVK analyses, NRSur7dq4 recovers a larger signal-to-noise ratio and/or Bayes factors for several events.

gr-qc↗

arXiv2025

Rapid stellar and binary population synthesis with COMPAS: methods paper II

The COMPAS public rapid binary population synthesis code has undergone a number of key improvements since the original COMPAS methods paper (Team COMPAS: Riley et al., 2022) was published. These include more sophisticated and robust treatments of binary interactions: mass transfer physics, common-envelope events, tides and gravitational-wave radiation reaction; and updated prescriptions for stellar evolution, winds and supernovae. The code structure and outputs have also been updated, with a focus on improving resolution without sacrificing computational speed. This paper describes the substantive changes in the code between the previous methods paper and COMPAS v03.22.01.

astro-ph.SR↗

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↗

arXiv2023

A follow-up on intermediate-mass black hole candidates in the second LIGO-Virgo observing run with the Bayes Coherence Ratio

The detection of an intermediate-mass black hole population ($10^2-10^6$ $M_{\odot}$) will provide clues to their formation environments (e.g., disks of active galactic nuclei, globular clusters) and illuminate a potential pathway to produce supermassive black holes. Ground-based gravitational-wave detectors are sensitive to mergers that can form intermediate-mass black holes weighing up to $\sim 450\ M_{\odot}$. However, ground-based detector data contain numerous incoherent short duration noise transients that can mimic the gravitational-wave signals from merging intermediate-mass black holes, limiting the sensitivity of searches. Here we follow-up on binary black hole merger candidates using a ranking statistic that measures the coherence or incoherence of triggers in multiple-detector data. We use this statistic to rank candidate events, initially identified by all-sky search pipelines, with lab-frame total masses $>55\ M_{\odot}$ using data from LIGO's second observing run. Our analysis does not yield evidence for new intermediate-mass black holes. However, we find support for eight stellar-mass binary black holes not reported in the first LIGO-Virgo gravitational wave transient catalog GWTC-1, seven of which have been previously reported by other catalogs.

gr-qc↗

arXiv2023

Measuring the properties of active galactic nuclei disks with gravitational waves

Active galactic nuclei (AGN) are promising environments for the assembly of merging binary black hole (BBH) systems. Interest in AGNs as nurseries for merging BBH is rising following the detection of gravitational waves from a BBH system from the purported pair-instability mass gap, most notably, GW190521. Active galactic nuclei have also been invoked to explain the formation of the high-mass-ratio system, GW190814. We draw on simulations of BBH systems in AGN to propose a phenomenological model for the distribution of black hole spins of merging binaries in AGN disks. The model incorporates distinct features that make the AGN channel potentially distinguishable from other channels, such as assembly in the field and in globular clusters. The model parameters can be mapped heuristically to the age and density of AGN disks. We estimate the extent to which different populations of mergers in AGNs can be distinguished. If most merging black holes are assembled in AGNs, future gravitational-wave observations may provide insights into the dynamics of AGN disks.

gr-qc↗

arXiv2023

Deep follow-up for gravitational-wave inference: a case study with GW151226

New analyses of gravitational wave events raise questions about the nature of some events. For example, LIGO--Virgo--KAGRA initially determined GW151226 to be a merger with a mass-ratio $q\approx0.5$ and effective inspiral spin $χ_{\text{eff}}\approx 0.2$. However, recent works offer an alternative picture: GW151226 is a lower-mass-ratio event $q \approx 0.3$ with slightly higher spin $χ_{\text{eff}}\approx 0.3$. This discrepancy has been challenging to resolve as a wide range of differences are employed for each analysis. This work introduces a ``deep follow-up'' framework to efficiently compute the posterior odds between two different peaks in parameter space. In doing so, we aim to help resolve disputes about the true nature of gravitational-wave events associated with conflicting astrophysical interpretations. Our proposal is not a replacement for standard inference techniques; instead, our method provides a diagnostic tool to understand discrepancies between conflicting results. We demonstrate this method by studying three {$q$-$χ_{\text{eff}}$} peaks proposed for GW151226. We find the $(q\sim0.5, χ_{\text{eff}}\sim0.2)$ interpretation is only slightly preferred over the $(q\sim0.3, χ_{\text{eff}}\sim0.3)$ hypothesis with a posterior odds of $\sim1.7\pm0.4$, suggesting that neither of the two peaks can be ruled out. We discuss strategies to produce more reliable parameter estimation studies in gravitational-wave astronomy.

astro-ph.HE↗

arXiv2021

GW190521 as a merger of Proca stars: a potential new vector boson of $8.7 \times 10^{-13}$ eV

Advanced LIGO-Virgo reported a short gravitational-wave signal (GW190521) interpreted as a quasi-circular merger of black holes, one populating the pair-instability supernova gap, forming a remnant black hole of $M_f\sim 142 M_\odot$ at a luminosity distance of $d_L \sim 5.3$ Gpc. With barely visible pre-merger emission, however, GW190521 merits further investigation of the pre-merger dynamics and even of the very nature of the colliding objects. We show that GW190521 is consistent with numerically simulated signals from head-on collisions of two (equal mass and spin) horizonless vector boson stars (aka Proca stars), forming a final black hole with $M_f = 231^{+13}_{-17}\,M_\odot$, located at a distance of $d_L = 571^{+348}_{-181}$ Mpc. The favoured mass for the ultra-light vector boson constituent of the Proca stars is $μ_{\rm V}= 8.72^{+0.73}_{-0.82}\times10^{-13}$ eV. This provides the first demonstration of close degeneracy between these two theoretical models, for a real gravitational-wave event. Confirmation of the Proca star interpretation, which we find statistically slightly preferred, would provide the first evidence for a long sought dark matter particle.

gr-qc↗

arXiv2020

Massively parallel Bayesian inference for transient gravitational-wave astronomy

Understanding the properties of transient gravitational waves and their sources is of broad interest in physics and astronomy. Bayesian inference is the standard framework for astro-physical measurement in transient gravitational-wave astronomy. Usually, stochastic sampling algorithms are used to estimate posterior probability distributions over the parameter spaces of models describing experimental data. The most physically accurate models typically come with a large computational overhead which can render data analysis extremely time consuming, or possibly even prohibitive. In some cases highly specialized optimizations can mitigate these issues, though they can be difficult to implement, as well as to generalize to arbitrary models of the data. Here, we propose an accurate, flexible and scalable method for astro-physical inference: parallelized nested sampling. The reduction in the wall-time of inference scales almost linearly with the number of parallel processes running on a high-performance computing cluster. By utilizing a pool of several hundreds or thousands of CPUs in a high-performance cluster, the large wall times of many astrophysical inferences can be alleviated while simultaneously ensuring that any gravitational-wave signal model can be used "out of the box", i.e., without additional optimization or approximation. Our method will be useful to both the LIGO-Virgo-KAGRA collaborations and the wider scientific community performing astrophysical analyses on gravitational waves. An implementation is available in the open source gravitational-wave inference library $\texttt{pBilby}$ (parallel $\texttt{bilby}$).

gr-qc↗

arXiv2018

Enhancing confidence in the detection of gravitational waves from compact binaries using signal coherence

We show that gravitational-wave signals from compact binary mergers may be better distinguished from instrumental noise transients by using Bayesian models that look for signal coherence across a detector network. This can be achieved even when the signal power is below the usual threshold for detection. This method could reject the vast majority of noise transients, and therefore increase sensitivity to weak gravitational waves. We demonstrate this using simulated signals, as well as data for GW150914 and LVT151012. Finally, we explore ways of incorporating our method into existing Advanced LIGO and Virgo searches to make them significantly more powerful.

gr-qc↗