arXiv subjects

Michael J. Williams

Publications and source records attributed to Michael J. Williams.

At least 19 recordsLinked to original sources

arXiv2026

Normalizing flows for density estimation in multi-detector gravitational-wave searches

Identifying compact binary coalescences buried within the non-Gaussian and non-stationary data taken by gravitational-wave interferometers requires sophisticated search pipelines, such as the PyCBC analysis. A critical task for these pipelines is determining the statistical significance of candidate events by comparing a "ranking statistic" against a large background set. Currently, PyCBC's ranking statistic incorporates the joint probability of the relative arrival times, phase delays and amplitude ratios of the signals seen in different detectors. These parameters are tightly constrained for physical signals but are more broadly distributed for noise. PyCBC currently relies on precomputed binned histogram-based density estimators using Monte-Carlo simulations to obtain these probabilities. However, the storage requirements for these histograms scale prohibitively with the size of the detector network, preventing PyCBC from effectively analyzing four or more detectors. In this paper, we demonstrate that these histograms can be replaced with normalizing flows, a machine learning approach to density estimation. Applying this method to data from the third observing run of Advanced LIGO and Virgo, we demonstrate that normalizing flows reduce storage requirements by over three orders of magnitude. Furthermore, our approach maintains high sensitivity, with less than a 0.05% drop in the recovery of simulated signals at a fixed false-alarm rate. By relaxing several simplifying assumptions previously required by Monte-Carlo methods, we also achieved up to a 6.55% increase in recovered signals for specific detector combinations. These results suggest that normalizing flows provide a scalable, flexible framework for the PyCBC pipeline as it expands to include four or more detectors, or to extend to searches for precessing or higher-mode signals, in future observing runs.

astro-ph.HE↗

arXiv2026

Leveraging rapid parameter estimates for efficient gravitational-wave Bayesian inference via posterior repartitioning

Gravitational-wave astronomy typically relies on rigorous, computationally expensive Bayesian analyses. Several methods have also been developed to perform rapid, approximate Bayesian inference. We present a novel approach to leverage the results of these low-latency analyses to accelerate the final inference, whilst ensuring that the Bayesian prior remains independent of the data. By combining the fast constraints from the \texttt{simple-pe} algorithm with the nested sampling acceleration technique of posterior repartitioning, we demonstrate that our method can guide the nested sampler towards the most probable regions of parameter space more efficiently for signal-to-noise ratios (SNR) greater than 20, while mathematically guaranteeing that the final inference is identical to that of a standard, uninformed analysis. We validate the method through an injection study on signals with SNR $<$ 150, demonstrating that it produces statistically robust and unbiased results whilst providing speedups of up to 210\%, with a mean speedup of 34\% for SNRs $>$ 20. Importantly, we show that the performance gain provided by our method scales with SNR, establishing it as a powerful technique to mitigate the cost of analysing signals from current and future gravitational-wave observatories.

gr-qc↗

arXiv2026

Inference with finite time series II: the window strikes back

Smooth window functions are often applied to strain data when inferring the parameters describing the astrophysical sources of gravitational-wave transients. Within the LIGO-Virgo-KAGRA collaboration, it is conventional to include a term to account for power loss due to this window in the likelihood function. We show that the inclusion of this factor leads to biased inference. The simplest solution to this, omitting the factor, leads to unbiased posteriors and Bayes factor estimates provided the window does not suppress the signal for signal-to-noise ratios $\lesssim O(100)$, but unreliable estimates of the absolute likelihood. Instead, we propose a multi-stage method that yields consistent estimates for the absolute likelihood in addition to unbiased posterior distributions and Bayes factors for signal-to-noise ratios $\lesssim O(1000)$. Additionally, we demonstrate that the commonly held wisdom that using rectangular windows necessarily leads to biased inference is incorrect.

gr-qc↗

arXiv2026

Accelerated Sequential Posterior Inference via Reuse for Gravitational-Wave Analyses

We introduce Accelerated Sequential Posterior Inference via Reuse (ASPIRE), a broadly applicable framework that transforms existing posterior samples and Bayesian evidence estimates into unbiased results under alternative models without rerunning the original analysis. ASPIRE combines normalizing flows with a generalized Sequential Monte Carlo (SMC) scheme, enabling efficient updates of existing results and reducing total likelihood evaluations and wall times by factors of up to 5.8 and 5.5, respectively, with larger gains per posterior sample. This addresses a growing problem in gravitational-wave astronomy, where events must be repeatedly reanalyzed under different models or physical hypotheses. We show that ASPIRE reproduces full Bayesian results when switching waveform models or adding physical effects such as spin precession and orbital eccentricity. With this statistical robustness, ASPIRE turns repeated reanalyses into fast, reliable updates-paving the way for systematic studies of waveform systematics, scalable reanalyses across large event catalogs, and broadly applicable Bayesian reanalysis across other scientific domains.

hep-ex↗

arXiv2026

Archival Inference for Eccentric Stellar-Mass Binary Black Holes in Space-Based Gravitational Wave Observations

Space-based gravitational-wave observatories will detect the early inspiral of stellar-mass binary black holes and can track their eccentricity evolution. However, untargeted searches in the space band are computationally demanding and require relatively high detection thresholds (signal-to-noise ratio $\sim 15$). Information from ground-based detections can significantly shrink the parameter space for space-band analyses and thereby substantially reduce the detection threshold. We present a Bayesian inference pipeline for ground-triggered archival space-band analyses that includes eccentricity. Using ground-informed priors, we demonstrate that with one year of LISA or TianQin data a GW190521-like source with signal-to-noise ratio $\sim 7$ can be distinguished and tightly constrained. In this setup, space observations sharpened the redshifted chirp mass from $\mathcal{O}(10^{-3})M_\odot$ to $\mathcal{O}(10^{-5})M_\odot$, and constrain the eccentricity to $\mathcal{O}(10^{-5})$ around the injected value $e_{0.01\mathrm{Hz}}=0.1$. These results demonstrate that inference of eccentric stellar-mass binary black holes in noisy space-band data is practically feasible, supports an expanded yield of multiband detections, and strengthens prospects for future astrophysical and gravitational tests.

astro-ph.HE↗

arXiv2025

Learning to detect continuous gravitational waves: an open data-analysis competition

We report results of a public data-analysis challenge, hosted on the open data-science platform Kaggle, to detect simulated continuous gravitational-wave signals (CWs). These are weak signals from rapidly spinning neutron stars that remain undetected despite extensive searches. The competition dataset consisted of a population of CW signals using both simulated and real LIGO detector data matching the conditions of actual CW searches. The competition attracted more than 1,000 participants to develop realistic CW search algorithms. We describe the top 10 approaches and discuss their applicability as a pre-processing step compared to standard CW-search approaches. For the competition's dataset, we find that top approaches can reduce the computing cost by 1 to 3 orders of magnitude at a false-dismissal probability comparable to standard CW searches. Additionally, the competition drove the development of new GPU-accelerated detection pipelines, which facilitated their adoption in other areas of gravitational-wave data analysis. We release the associated dataset, which constitutes the first open standardized benchmark for CW detection, to enable reproducible method comparisons and to encourage further developments toward the first detection of these elusive signals.

gr-qc↗

arXiv2025

Multiband parameter estimation with phase coherence and extrinsic marginalization: Extracting more information from low-SNR CBC signals in LISA data

This paper presents a novel coherent multiband analysis framework for characterizing stellar- and intermediate-mass binary black holes using LISA and next-generation ground-based detectors (ET and CE), leveraging the latest developments in the \texttt{PyCBC} pipeline. Given the population parameters inferred from LVK results and LISA's sensitivity limits at high frequencies, most stellar-mass binary black holes would likely have SNRs below 5 in LISA, but the most state-of-the-art multiband parameter estimation methods, such as those using ET and CE posteriors as priors for LISA, typically struggle to analyze sources with a LISA SNR less than 5. We present a novel coherent multiband parameter estimation method that directly calculates a joint likelihood, which is highly efficient; this efficiency is enabled by multiband marginalization of the extrinsic parameter space, implemented using importance sampling, which can work robustly even when the LISA SNR is as low as 3. Having an SNR of $\sim 3$ allows LISA to contribute nearly double the number of multiband sources. Even if LISA only observes for one year, most of the multiband detector-frame chirp mass's 90\% credible interval (less than $10^{-4} \mathrm{M}_\odot$) is still better than that of the most accurately measured events for ET+2CE network in 7.5 years of observation, by at least one order of magnitude. For the first time, we show efficient multiband Bayesian parameter estimation results on the population scale, which paves the way for large-scale astrophysical tests using multibanding.

gr-qc↗

arXiv2025

Validating Sequential Monte Carlo for Gravitational-Wave Inference

Nested sampling (NS) is the preferred stochastic sampling algorithm for gravitational-wave inference for compact binary coalenscences (CBCs). It can handle the complex nature of the gravitational-wave likelihood surface and provides an estimate of the Bayesian model evidence. However, there is another class of algorithms that meets the same requirements but has not been used for gravitational-wave analyses: Sequential Monte Carlo (SMC), an extension of importance sampling that maps samples from an initial density to a target density via a series of intermediate densities. In this work, we validate a type of SMC algorithm, called persistent sampling (PS), for gravitational-wave inference. We consider a range of different scenarios including binary black holes (BBHs) and binary neutron stars (BNSs) and real and simulated data and show that PS produces results that are consistent with NS whilst being, on average, 2 times more efficient and 2.74 times faster. This demonstrates that PS is a viable alternative to NS that should be considered for future gravitational-wave analyses.

astro-ph.IM↗

arXiv2025

Use of Bayesian Inference to Diagnose Issues in Experimental Measurements of Mechanical Disk Resonators

Gravitational wave detectors, such as LIGO, are predominantly limited by coating Brownian thermal noise (CTN), arising from mechanical losses in the Bragg mirror coatings used on test-mass optics. Accurately characterizing and minimizing these losses is crucial for enhancing detector sensitivity. This paper introduces a general mathematical and statistical framework leveraging Bayesian inference to precisely analyse mechanical ring-down measurements of disk resonators, a standard method for quantifying mechanical loss in coating materials. Our approach presents a refined model that fully captures the non-linear behaviour of beam spot motion on split photodiode sensors, significantly improving upon traditional simplified exponential-decay methods. We achieve superior estimation accuracy for decay constants ($τ_1$ and $τ_2$), especially for measurements exhibiting larger oscillation amplitudes. Specifically, we observe improvements in estimation accuracy by up to 25$\%$ over traditional methods, with strong Bayesian evidence favouring our framework. Our simulations and experimental validations reveal that previously discarded measurements due to fitting inaccuracies can now be reliably analysed, maximizing the use of available data. This enhanced analytical capability not only provides more precise mechanical loss estimations but also offers deeper insights into systematic issues affecting disk resonator measurements, paving the way toward improved coating materials and ultimately, more sensitive gravitational wave detectors.

physics.ins-det↗

arXiv2024

First investigation of void statistics in numerical relativity simulations

We apply and extend standard tools for void statistics to cosmological simulations that solve Einstein's equations with numerical relativity (NR). We obtain a simulated void catalogue without Newtonian approximations, using a new watershed void finder which operates on fluid-based NR simulations produced with the Einstein Toolkit. We compare and contrast measures of void size and void fraction, and compare radial stacked density profiles to empirically-derived Hamaus-Sutter-Wandelt (HSW) density profiles and profiles based on distance to void boundaries. We recover statistics roughly consistent with Newtonian N-body simulations where such a comparison is meaningful. We study variation of dynamical spatial curvature and local expansion explicitly demonstrating the spatial fluctuations of these quantities in void regions. We find that voids in our simulations expand ~10-30% faster than the global average and the spatial curvature density parameter in the centre of voids reaches ~60-80%.

astro-ph.CO↗

arXiv2024

Premerger observation and characterization of massive black hole binaries

We demonstrate an end-to-end technique for observing and characterizing massive black hole binary signals before they merge with the LISA space-based gravitational-wave observatory. Our method uses a zero-latency whitening filter, originally designed for rapidly observing compact binary mergers in ground-based observatories, to be able to observe signals with no additional latency due to filter length. We show that with minimal computational cost, we are able to reliably observe signals as early as 14 days premerger as long as the signal has accrued a signal-to-noise ratio of at least 8 in the LISA data. We also demonstrate that this method can be used to characterize the source properties, providing early estimates of the source's merger time, chirp mass, and sky localization. Early observation and characterization of massive black holes is crucial to enable the possibility of rapid multimessenger observations, and to ensure that LISA can enter a protected operating period when the merger signal arrives.

hep-ex↗

arXiv2024

Rapid neutron star equation of state inference with Normalising Flows

The first direct detection of gravitational waves from binary neutron stars on the 17th of August, 2017, (GW170817) heralded the arrival of a new messenger for probing neutron star astrophysics and provided the first constraints on neutron star equation of state from gravitational wave observations. Significant computational effort was expended to obtain these first results and therefore, as observations of binary neutron star coalescence become more routine in the coming observing runs, there is a need to improve the analysis speed and flexibility. Here, we present a rapid approach for inferring the neutron star equation of state based on Normalising Flows. As a demonstration, using the same input data, our approach, ASTREOS, produces results consistent with those presented by the LIGO-Virgo collaboration but requires < 1 sec to generate neutron star equation of state confidence intervals. Furthermore, ASTREOS allows for non-parametric equation of state inference. This rapid analysis will not only facilitate neutron star equation of state studies but can potentially enhance future alerts for electromagnetic follow-up observations of binary neutron star mergers.

gr-qc↗

arXiv2023

Rapid Generation of Kilonova Light Curves Using Conditional Variational Autoencoder

The discovery of the optical counterpart, along with the gravitational waves from GW170817, of the first binary neutron star merger, opened up a new era for multi-messenger astrophysics. Combining the GW data with the optical counterpart, also known as AT2017gfo, classified as a kilonova, has revealed the nature of compact binary merging systems by extracting enriched information about the total binary mass, the mass ratio, the system geometry, and the equation of state. Even though the detection of kilonova brought about a revolution in the domain of multi-messenger astronomy, since there has been only one kilonova from a gravitational wave detected binary neutron star merger event so far, this limits the exact understanding of the origin and propagation of the kilonova. Here, we use a conditional variational autoencoder trained on light curve data from two kilonova models having different temporal lengths, and consequently, generate kilonova light curves rapidly based on physical parameters of our choice with good accuracy. Once trained, the time scale for light curve generation is of the order of a few milliseconds, thus speeding up generating light curves by $1000$ times compared to the simulation. The mean squared error between the generated and original light curves is typically $0.015$ with a maximum of $0.08$ for each set of considered physical parameter; while having a maximum of $\approx0.6$ error across the whole parameter space. Hence, implementing this technique provides fast and reliably accurate results.

astro-ph.HE↗

arXiv2023

Importance nested sampling with normalising flows

We present an improved version of the nested sampling algorithm nessai in which the core algorithm is modified to use importance weights. In the modified algorithm, samples are drawn from a mixture of normalising flows and the requirement for samples to be independently and identically distributed (i.i.d.) according to the prior is relaxed. Furthermore, it allows for samples to be added in any order, independently of a likelihood constraint, and for the evidence to be updated with batches of samples. We call the modified algorithm i-nessai. We first validate i-nessai using analytic likelihoods with known Bayesian evidences and show that the evidence estimates are unbiased in up to 32 dimensions. We compare i-nessai to standard nessai for the analytic likelihoods and the Rosenbrock likelihood, the results show that i-nessai is consistent with nessai whilst producing more precise evidence estimates. We then test i-nessai on 64 simulated gravitational-wave signals from binary black hole coalescence and show that it produces unbiased estimates of the parameters. We compare our results to those obtained using standard nessai and dynesty and find that i-nessai requires 2.68 and 13.3 times fewer likelihood evaluations to converge, respectively. We also test i-nessai of an 80-second simulated binary neutron star signal using a Reduced-Order-Quadrature (ROQ) basis and find that, on average, it converges in 24 minutes, whilst only requiring $1.01\times10^6$ likelihood evaluations compared to $1.42\times10^6$ for nessai and $4.30\times10^7$ for dynesty. These results demonstrate the i-nessai is consistent with nessai and dynesty whilst also being more efficient.

astro-ph.IM↗

arXiv2023

Unpacking merger jets: a Bayesian analysis of GW170817, GW190425 and electromagnetic observations of short gamma-ray bursts

We present a novel fully Bayesian analysis to constrain short gamma-ray burst jet structures associated with cocoon, wide-angle and simple top-hat jet models, as well as the binary neutron star merger rate. These constraints are made given the distance and inclination information from GW170817, observed flux of GRB170817A, observed rate of short gamma-ray bursts detected by Swift, and the neutron star merger rate inferred from LIGO's first and second observing runs. A separate analysis is conducted where a fitted short gamma-ray burst luminosity function is included to provide further constraints. The jet structure models are further constrained using the observation of GW190425 and we find that the assumption that it produced a GRB170817-like short gamma-ray burst that went undetected due to the jet geometry is consistent with previous observations. We find and quantify evidence for low luminosity and wide-angled jet structuring in the short gamma-ray burst population, independently from afterglow observations, with log Bayes factors of $0.45{-}0.55$ for such models when compared to a classical top-hat jet. Slight evidence is found for a Gaussian jet structure model over all others when the fitted luminosity function is provided, producing log Bayes factors of $0.25{-}0.9\pm0.05$ when compared to the other models. However without considering GW190425 or the fitted luminosity function, the evidence favours a cocoon-like model with log Bayes factors of $0.14\pm0.05$ over the Gaussian jet structure. We provide new constraints to the binary neutron star merger rates of $1{-}1300$Gpc$^{-3}$yr$^{-1}$ or $2{-}680$Gpc$^{-3}$yr$^{-1}$ when a fitted luminosity function is assumed.

astro-ph.HE↗

arXiv2021

A Bayesian Inference Framework for Gamma-Ray Burst Afterglow Properties

In the field of multi-messenger astronomy, Bayesian inference is commonly adopted to compare the compatibility of models given the observed data. However, to describe a physical system like neutron star mergers and their associated gamma-ray burst (GRB) events, usually more than ten physical parameters are incorporated in the model. With such a complex model, likelihood evaluation for each Monte Carlo sampling point becomes a massive task and requires a significant amount of computational power. In this work, we perform quick parameter estimation on simulated GRB X-ray light curves using an interpolated physical GRB model. This is achieved by generating a grid of GRB afterglow light curves across the parameter space and replacing the likelihood with a simple interpolation function in the high-dimensional grid that stores all light curves. This framework, compared to the original method, leads to a $\sim$90$\times$ speedup per likelihood estimation. It will allow us to explore different jet models and enable fast model comparison in the future.

astro-ph.HE↗

arXiv2021

Nested Sampling with Normalising Flows for Gravitational-Wave Inference

We present a novel method for sampling iso-likelihood contours in nested sampling using a type of machine learning algorithm known as normalising flows and incorporate it into our sampler nessai. Nessai is designed for problems where computing the likelihood is computationally expensive and therefore the cost of training a normalising flow is offset by the overall reduction in the number of likelihood evaluations. We validate our sampler on 128 simulated gravitational wave signals from compact binary coalescence and show that it produces unbiased estimates of the system parameters. Subsequently, we compare our results to those obtained with dynesty and find good agreement between the computed log-evidences whilst requiring 2.07 times fewer likelihood evaluations. We also highlight how the likelihood evaluation can be parallelised in nessai without any modifications to the algorithm. Finally, we outline diagnostics included in nessai and how these can be used to tune the sampler's settings.

gr-qc↗

arXiv2014

Central rotations of Milky Way Globular Clusters

Most Milky Way globular clusters (GCs) exhibit measurable flattening, even if on a very low level. Both cluster rotation and tidal fields are thought to cause this flattening. Nevertheless, rotation has only been confirmed in a handful of GCs, based mostly on individual radial velocities at large radii. We are conducting a survey of the central kinematics of Galactic GCs using the new Integral Field Unit instrument VIRUS-W. We detect rotation in all 11 GCs that we have observed so far, rendering it likely that a large majority of the Milky Way GCs rotate. We use published catalogs of the ACS survey of GCs to derive central ellipticities and position angles. We show that in all cases where the central ellipticity permits an accurate measurement of the position angle, those angles are in excellent agreement with the kinematic position angles that we derive from the VIRUS-W velocity fields. We find an unexpected tight correlation between central rotation and outer ellipticity, indicating that rotation drives flattening for the objects in our sample. We also find a tight correlation between central rotation and published values for the central velocity dispersion, most likely due to rotation impacting the old dispersion measurements.

astro-ph.GA↗