Alvin J. K. Chua

Efficient sampling from high-dimensional, multi-modal posteriors is a central challenge in Bayesian inference across the physical sciences. Gravitational-wave (GW) astronomy, where likelihood evaluations are computationally expensive and posteriors are complex, is one application motivating this work. Popular families of methods like Markov-chain Monte Carlo, Snested sampling, and importance sampling (IS) all rely on proposal distributions to guide exploration. Because prior knowledge of the target is often limited, practitioners can adopt adaptive proposals that iteratively refine themselves using information gained from previously drawn samples. Traditional adaptive strategies, however, struggle in high-dimensional multi-modal settings: complex, non-linear correlations are hard to capture, and hyperparameters typically require tedious, problem-specific tuning. To address these issues, we introduce parallel adaptive reweighting IS (PARIS; descriptively, ‘seed sampling’). PARIS models its proposal as a Gaussian mixture whose component centers are the existing samples and whose component weights match the current importance weights. New draws from the proposal therefore concentrate around high-weight regions, while candidate points in unexplored areas receive intentionally inflated weights. As the algorithm continuously reweights all samples up to the latest proposal, any initial over-weighting self-corrects once additional neighbor samples are collected. To enable rapid reweighting, we present an efficient update scheme and evaluate PARIS on illustrative toy problems and more realistic GW parameter estimation tasks. PARIS achieves accurate posterior reconstruction and evidence estimation with substantially fewer function evaluations than competing approaches, highlighting its promise for widespread use in astrophysical data analysis.

Extreme mass ratio inspirals (EMRIs) are key sources for the future space-based gravitational wave detector Laser Interferometer Space Antenna (LISA) and are considered promising probes of fundamental physics. Here, we present the first complete Bayesian analysis of EMRI signals in theories with an additional massless scalar, which could arise in an extension of general relativity or of the Standard Model of particle physics. We develop a waveform model accurate at adiabatic order for equatorial eccentric orbits around spinning black holes. Using full Bayesian inference, we forecast LISA’s ability to probe the presence of new fundamental fields with EMRI observations.

Observations of gravitational-wave signals emitted by compact binary inspirals provide unique insights into their properties, but their analysis requires accurate and efficient waveform models. Intermediate- and extreme-mass-ratio inspirals (I/EMRIs), with mass ratios q ≳ 10 2 , are promising sources for future detectors such as the Laser Interferometer Space Antenna (LISA). Modeling waveforms for these asymmetric-mass binaries is challenging, entailing the tracking of many harmonic modes over thousands to millions of cycles. The FastEMRIWaveforms () modeling framework addresses this need, leveraging precomputation of mode data and interpolation to rapidly compute adiabatic waveforms for eccentric inspirals into zero-spin black holes. In this work, we extend to model eccentric equatorial inspirals into black holes with spin magnitudes | a | ≤ 0.999 . Our model supports eccentricities e ≤ 0.9 and semilatus recta p ≤ 200 , enabling the generation of long-duration IMRI waveforms, and produces waveforms in ∼ 100 ms with hardware acceleration. Characterizing systematic errors, we estimate that our model attains mismatches of ∼ 10 − 5 (for LISA sensitivity) with respect to error-free adiabatic waveforms over the majority of the parameter space. We find that kludge models can introduce errors in signal-to-noise ratios (SNRs) as great as − 40 % + 60 % and induce marginal biases of up to ∼ 1 σ in parameter estimation. We show that LISA’s horizon redshift for I/EMRI signals varies significantly with a , reaching a redshift of 3 (15) for EMRIs (IMRIs) with only minor ( ∼ 10 % ) dependence on e for an SNR threshold of 20. For signals with SNR ∼ 50 , spin and eccentricity at plunge are measured with uncertainties of δ a ∼ 10 − 7 and δ e f ∼ 10 − 5 . This work advances the state of the art in waveform generation for asymmetric-mass binaries, providing open-source tools for the investigation of I/EMRI astrophysics and data analysis.

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the early inspirals of stellar-mass black holes that will ultimately venture into the ground-based detectors’ view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA’s discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This White Paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

Extreme-mass-ratio inspirals (EMRIs) are one of the primary targets for the recently adopted millihertz gravitational-wave (GW) observatory LISA. Some previous studies have argued that a fraction of all EMRIs form in matter-rich environments, and can potentially explain the dozens of soft X-ray band (⁠|$\sim 10^{-1} \rm keV$|⁠), low-frequency (∼0.1 mHz) periodic phenomena known as quasi-periodic eruptions (QPEs) and quasi-periodic oscillations (QPOs). Here, using a representative EMRI population retrofitted with cutoffs on LISA-band SNRs and luminosity distances to account for the sensitivity of current instruments, we estimate the mean frequency band in which QPEs and QPOs originating from detectable LISA EMRIs may be emitting an X-ray signal “today” (i.e., in 2024) to be 0.46 ± 0.22 mHz. We also model the well-known QPO source, RE J1034+396, which falls in this frequency band, as an EMRI assuming its primary black hole mass to be 10⁶ − 10⁷M_⊙. Through a prior-predictive analysis, we estimate the orbiting compact object’s mass to be |$46^{+ 10}_{-40} M_\odot$| and the source’s LISA-band SNR as ≈14, highlighting it as a candidate multi-messenger EMRI target. We also highlight the role of current and near-future X-ray and UV observatories in enabling multi-messenger observations of EMRIs in conjunction with LISA, and conclude with a discussion of caveats of the current analysis, such as the exclusion of eccentricity and inclination from the model, and the measurability of sub-solar mass compact object EMRIs.

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 simulations. Such approximations can generally lead to an inaccurate posterior distribution with poor statistical coverage of the true posterior. In this paper, 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.