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Bayesian inference has many advantages for complex models, but standard Monte Carlo methods for summarizing the posterior can be computationally demanding, and it is attractive to consider optimization-based variational methods. Our work…

Computation · Statistics 2025-10-09 Aoxiang Chen , David J. Nott , Linda S. L. Tan

Gaussian Random Fields (GRFs) with Mat\'ern covariance functions have emerged as a powerful framework for modeling spatial processes due to their flexibility in capturing different features of the spatial field. However, the smoothness…

Computation · Statistics 2026-01-19 Yiping Hong , Sameh Abdulah , Marc G. Genton , Ying Sun

The GstLAL library, derived from Gstreamer and the LIGO Algorithm Library, supports a stream-based approach to gravitational-wave data processing. Although GstLAL was primarily designed to search for gravitational-wave signatures of merging…

Assuming a Euclid-like weak lensing data set, we compare different methods of dealing with its inherent parameter degeneracies. Including priors into a data analysis can mask the information content of a given data set alone. However, since…

Cosmology and Nongalactic Astrophysics · Physics 2016-01-27 Elena Sellentin , Björn Malte Schäfer

Space-borne gravitational wave detectors will expand the scope of gravitational wave astronomy to the milli-Hertz band in the near future. The development of data analysis software infrastructure at the current stage is crucial. In this…

General Relativity and Quantum Cosmology · Physics 2026-02-13 Rui Niu , Chang Feng , Wen Zhao

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…

General Relativity and Quantum Cosmology · Physics 2024-04-03 Ruiting Mao , Jeong Eun Lee , Ollie Burke , Alvin J. K. Chua , Matthew C. Edwards , Renate Meyer

Unlike ground-based gravitational wave detectors, space-based gravitational wave detectors can detect the ringdown signals from massive black hole mergers with large signal-to-noise ratios, help to localize sources and extract their…

General Relativity and Quantum Cosmology · Physics 2021-11-01 Chunyu Zhang , Yungui Gong , Chao Zhang

Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters - both their errors and covariances. In this short review, I outline a…

Cosmology and Nongalactic Astrophysics · Physics 2016-08-24 Alan Heavens

Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…

Statistics Theory · Mathematics 2023-01-05 Yuling Yan , Kaizheng Wang , Philippe Rigollet

Direct detection of gravitational waves by pulsar timing arrays will become feasible over the next few years. In the low frequency regime ($10^{-7}$ Hz -- $10^{-9}$ Hz), we expect that a superposition of gravitational waves from many…

Instrumentation and Methods for Astrophysics · Physics 2015-06-15 Justin Ellis , Xavier Siemens , Rutger van Haasteren

In the gravitational-wave analysis of pulsar-timing-array datasets, parameter estimation is usually performed using Markov Chain Monte Carlo methods to explore posterior probability densities. We introduce an alternative procedure that…

General Relativity and Quantum Cosmology · Physics 2024-05-16 Michele Vallisneri , Marco Crisostomi , Aaron D. Johnson , Patrick M. Meyers

We present a kernel-independent method that applies hierarchical matrices to the problem of maximum likelihood estimation for Gaussian processes. The proposed approximation provides natural and scalable stochastic estimators for its…

Computation · Statistics 2019-03-26 Christopher J. Geoga , Mihai Anitescu , Michael L. Stein

We derive a Fisher matrix for the parameters characterising a population of gravitational-wave events. This provides a guide to the precision with which population parameters can be estimated with multiple observations, which becomes…

General Relativity and Quantum Cosmology · Physics 2022-12-14 Jonathan R. Gair , Andrea Antonelli , Riccardo Barbieri

To evaluate the probability of a gravitational-wave candidate originating from noise, GstLAL collects noise statistics from the data it analyzes. Gravitational-wave signals of astrophysical origin get added to the noise statistics, harming…

General Relativity and Quantum Cosmology · Physics 2023-05-30 Prathamesh Joshi , Leo Tsukada , Chad Hanna

In this paper, we develop a Neural Likelihood Estimator and apply it to analyse real gravitational-wave (GW) data for the first time. We assess the usability of neural likelihood for GW parameter estimation and report the parameter space…

High Energy Astrophysical Phenomena · Physics 2025-09-23 Luca Negri , Anuradha Samajdar

We introduce $\texttt{GWFAST}$, a novel Fisher-matrix code for gravitational-wave studies, tuned toward third-generation gravitational-wave detectors such as Einstein Telescope (ET) and Cosmic Explorer (CE). We use it to perform a…

General Relativity and Quantum Cosmology · Physics 2023-01-02 Francesco Iacovelli , Michele Mancarella , Stefano Foffa , Michele Maggiore

The copious scientific literature produced after the detection of GW170817 electromagnetic counterpart demonstrated the importance of a prompt and accurate localization of the gravitational wave within the co-moving volume. In this letter,…

Instrumentation and Methods for Astrophysics · Physics 2022-09-14 Stefano Rinaldi , Walter Del Pozzo

A joint fit of the mass and redshift distributions of the population of Binary Black Holes detected with Gravitational-Wave observations can be used to obtain constraints on the Hubble parameter and on deviations from General Relativity in…

General Relativity and Quantum Cosmology · Physics 2022-11-29 Michele Mancarella , Nicola Borghi , Stefano Foffa , Edwin Genoud-Prachex , Francesco Iacovelli , Michele Maggiore , Michele Moresco , Matteo Schulz

Gravitational wave (GW) observations probe both a diffuse, stochastic gravitational wave background (SGWB) as well as individual cataclysmic events such as the merger of two compact objects. The detection and description of the…

Cosmology and Nongalactic Astrophysics · Physics 2025-03-28 Eleanor Gleave , Andrew Jaffe

Owing to the forecasted improved sensitivity of ground-based gravitational-wave detectors, new research avenues will become accessible. This is the case for gravitational-wave strong lensing, predicted with a non-negligible observation rate…

General Relativity and Quantum Cosmology · Physics 2023-10-18 Justin Janquart , K. Haris , Otto A. Hannuksela , Chris Van Den Broeck