nested-sampling.bib

@article{ashtonNestedSamplingPhysical2022,
  title = {Nested Sampling for Physical Scientists},
  author = {Ashton, Greg and Bernstein, Noam and Buchner, Johannes and Chen, Xi and Csányi, Gábor and Fowlie, Andrew and Feroz, Farhan and Griffiths, Matthew and Handley, Will and Habeck, Michael and Higson, Edward and Hobson, Michael and Lasenby, Anthony and Parkinson, David and Pártay, Livia B. and Pitkin, Matthew and Schneider, Doris and Speagle, Joshua S. and South, Leah and Veitch, John and Wacker, Philipp and Wales, David J. and Yallup, David},
  date = {2022-05-26},
  journaltitle = {Nature Reviews Methods Primers},
  shortjournal = {Nat Rev Methods Primers},
  volume = {2},
  number = {1},
  pages = {1--22},
  publisher = {Nature Publishing Group},
  issn = {2662-8449},
  doi = {10.1038/s43586-022-00121-x},
  url = {https://www.nature.com/articles/s43586-022-00121-x},
  urldate = {2024-11-23},
  abstract = {This Primer examines Skilling’s nested sampling algorithm for Bayesian inference and, more broadly, multidimensional integration. The principles of nested sampling are summarized and recent developments using efficient nested sampling algorithms in high dimensions~surveyed, including methods for sampling from the constrained prior. Different ways of applying nested sampling are outlined, with detailed examples from three scientific fields: cosmology, gravitational-wave astronomy and materials science. Finally, the Primer includes recommendations for best practices and a discussion of potential limitations and optimizations of nested sampling.},
  langid = {english},
  keywords = {Statistical physics,Statistics},
  file = {/home/jacopo/Zotero/storage/78F2DMGC/Ashton et al. - 2022 - Nested sampling for physical scientists.pdf}
}

@book{billingsleyProbabilityMeasure1995,
  title = {Probability and Measure},
  author = {Billingsley, Patrick},
  date = {1995},
  series = {Wiley Series in Probability and Mathematical Statistics},
  edition = {3. ed},
  publisher = {Wiley},
  location = {New York, NY},
  isbn = {978-0-471-00710-4},
  langid = {english},
  pagetotal = {593},
  file = {/home/jacopo/Zotero/storage/5JS2GV7Y/Billingsley - 1995 - Probability and measure.pdf}
}

@online{buchnerIntuitionPhysicistsInformation2022,
  title = {An Intuition for Physicists: Information Gain from Experiments},
  shorttitle = {An Intuition for Physicists},
  author = {Buchner, Johannes},
  date = {2022-08-26},
  eprint = {2205.00009},
  eprinttype = {arXiv},
  eprintclass = {astro-ph, physics:cond-mat, physics:physics},
  doi = {10.48550/arXiv.2205.00009},
  url = {http://arxiv.org/abs/2205.00009},
  urldate = {2024-05-29},
  abstract = {How much one has learned from an experiment is quantifiable by the information gain, also known as the Kullback-Leibler divergence. The narrowing of the posterior parameter distribution \$P(\textbackslash theta|D)\$ compared with the prior parameter distribution \$\textbackslash pi(\textbackslash theta)\$, is quantified in units of bits, as: \$ D\_\{\textbackslash mathrm\{KL\}\}(P|\textbackslash pi)=\textbackslash int\textbackslash log\_\{2\}\textbackslash left(\textbackslash frac\{P(\textbackslash theta|D)\}\{\textbackslash pi(\textbackslash theta)\}\textbackslash right)\textbackslash,P(\textbackslash theta|D)\textbackslash,d\textbackslash theta \$. This research note gives an intuition what one bit of information gain means. It corresponds to a Gaussian shrinking its standard deviation by a factor of three.},
  pubstate = {prepublished},
  version = {3},
  keywords = {Astrophysics - Instrumentation and Methods for Astrophysics,Condensed Matter - Statistical Mechanics,Physics - Data Analysis Statistics and Probability},
  file = {/home/jacopo/Zotero/storage/8RW7LGYW/Buchner - 2022 - An intuition for physicists information gain from.pdf;/home/jacopo/Zotero/storage/D27ZDLT4/2205.html}
}

@unpublished{buchnerNestedSamplingMethods2021,
  title = {Nested {{Sampling Methods}}},
  author = {Buchner, Johannes},
  date = {2021-07-13},
  eprint = {2101.09675},
  eprinttype = {arXiv},
  eprintclass = {astro-ph, stat},
  url = {http://arxiv.org/abs/2101.09675},
  urldate = {2021-10-19},
  abstract = {Nested sampling (NS) computes parameter posterior distributions and makes Bayesian model comparison computationally feasible. Its strengths are the unsupervised navigation of complex, potentially multi-modal posteriors until a well-defined termination point. A systematic literature review of nested sampling algorithms and variants is presented. We focus on complete algorithms, including solutions to likelihood-restricted prior sampling, parallelisation, termination and diagnostics. The relation between number of live points, dimensionality and computational cost is studied for two complete algorithms. A new formulation of NS is presented, which casts the parameter space exploration as a search on a tree. Previously published ways of obtaining robust error estimates and dynamic variations of the number of live points are presented as special cases of this formulation. A new on-line diagnostic test is presented based on previous insertion rank order work. The survey of nested sampling methods concludes with outlooks for future research.},
  keywords = {Astrophysics - Instrumentation and Methods for Astrophysics,Statistics - Computation},
  file = {/home/jacopo/Zotero/storage/PUU2NMMQ/Buchner_2021_Nested Sampling Methods.pdf;/home/jacopo/Zotero/storage/GCVJUHDH/2101.html}
}

@online{buchnerRelativeJumpDistance2024,
  title = {Relative {{Jump Distance}}: A Diagnostic for {{Nested Sampling}}},
  shorttitle = {Relative {{Jump Distance}}},
  author = {Buchner, Johannes},
  date = {2024-02-19},
  eprint = {2402.11936},
  eprinttype = {arXiv},
  eprintclass = {stat},
  doi = {10.48550/arXiv.2402.11936},
  url = {http://arxiv.org/abs/2402.11936},
  urldate = {2024-12-12},
  abstract = {Nested sampling is widely used in astrophysics for reliably inferring model parameters and comparing models within a Bayesian framework. To address models with many parameters, Markov Chain Monte Carlo (MCMC) random walks are incorporated within nested sampling to advance a live point population. Diagnostic tools for nested sampling are crucial to ensure the reliability of astrophysical conclusions. We develop a diagnostic to identify problematic random walks that fail to meet the requirements of nested sampling. The distance from the start to the end of the random walk, the jump distance, is divided by the typical neighbor distance between live points, computed robustly with the MLFriends algorithm, to obtain a relative jump distance (RJD). We propose the geometric mean RJD and the fraction of RJD{$>$}1 as new summary diagnostics. Relative jump distances are investigated with mock and real-world inference applications, including inferring the distance to gravitational wave event GW170817. Problematic nested sampling runs are identified based on significant differences to reruns with much longer MCMC chains. These consistently exhibit low average RJDs and f(RJD{$>$}1) values below 50 percent. The RJD is more sensitive than previous tests based on the live point insertion order. The RJD diagnostic is proposed as a widely applicable diagnostic to verify inference with nested sampling. It is implemented in the UltraNest package in version 4.1.},
  pubstate = {prepublished},
  keywords = {Astrophysics - Instrumentation and Methods for Astrophysics,Statistics - Methodology},
  file = {/home/jacopo/Zotero/storage/IURHSRYD/Buchner - 2024 - Relative Jump Distance a diagnostic for Nested Sa.pdf;/home/jacopo/Zotero/storage/VMJVHFKA/2402.html}
}

@online{burkeMindGapAddressing2025,
  title = {Mind the Gap: Addressing Data Gaps and Assessing Noise Mismodeling in {{LISA}}},
  shorttitle = {Mind the Gap},
  author = {Burke, Ollie and Marsat, Sylvain and Gair, Jonathan R. and Katz, Michael L.},
  date = {2025-02-24},
  eprint = {2502.17426},
  eprinttype = {arXiv},
  eprintclass = {gr-qc},
  doi = {10.48550/arXiv.2502.17426},
  url = {http://arxiv.org/abs/2502.17426},
  urldate = {2025-02-26},
  abstract = {Due to the sheer complexity of the Laser Interferometer Space Antenna (LISA) space mission, data gaps arising from instrumental irregularities and/or scheduled maintenance are unavoidable. Focusing on merger-dominated massive black hole binary signals, we test the appropriateness of the Whittle-likelihood on gapped data in a variety of cases. From first principles, we derive the likelihood valid for gapped data in both the time and frequency domains. Cheap-to-evaluate proxies to p-p plots are derived based on a Fisher-based formalism, and verified through Bayesian techniques. Our tools allow to predict the altered variance in the parameter estimates that arises from noise mismodeling, as well as the information loss represented by the broadening of the posteriors. The result of noise mismodeling with gaps is sensitive to the characteristics of the noise model, with strong low-frequency (red) noise and strong high-frequency (blue) noise giving statistically significant fluctuations in recovered parameters. We demonstrate that the introduction of a tapering window reduces statistical inconsistency errors, at the cost of less precise parameter estimates. We also show that the assumption of independence between inter-gap segments appears to be a fair approximation even if the data set is inherently coherent. However, if one instead assumes fictitious correlations in the data stream, when the data segments are actually independent, then the resultant parameter recoveries could be inconsistent with the true parameters. The theoretical and numerical practices that are presented in this work could readily be incorporated into global-fit pipelines operating on gapped data.},
  pubstate = {prepublished},
  keywords = {Astrophysics - High Energy Astrophysical Phenomena,Astrophysics - Instrumentation and Methods for Astrophysics,General Relativity and Quantum Cosmology},
  file = {/home/jacopo/Zotero/storage/942977CX/Burke et al. - 2025 - Mind the gap addressing data gaps and assessing n.pdf;/home/jacopo/Zotero/storage/DWXPBN38/2502.html}
}

@online{chenBayesianPosteriorRepartitioning2022,
  title = {Bayesian Posterior Repartitioning for Nested Sampling},
  author = {Chen, Xi and Feroz, Farhan and Hobson, Michael},
  date = {2022-07-04},
  eprint = {1908.04655},
  eprinttype = {arXiv},
  doi = {10.48550/arXiv.1908.04655},
  url = {http://arxiv.org/abs/1908.04655},
  urldate = {2024-11-27},
  abstract = {Priors in Bayesian analyses often encode informative domain knowledge that can be useful in making the inference process more efficient. Occasionally, however, priors may be unrepresentative of the parameter values for a given dataset, which can result in inefficient parameter space exploration, or even incorrect inferences, particularly for nested sampling (NS) algorithms. Simply broadening the prior in such cases may be inappropriate or impossible in some applications. Hence our previous solution to this problem, known as posterior repartitioning (PR), redefines the prior and likelihood while keeping their product fixed, so that the posterior inferences and evidence estimates remain unchanged, but the efficiency of the NS process is significantly increased. In its most practical form, PR raises the prior to some power beta, which is introduced as an auxiliary variable that must be determined on a case-by-case basis, usually by lowering beta from unity according to some pre-defined `annealing schedule' until the resulting inferences converge to a consistent solution. Here we present a very simple yet powerful alternative Bayesian approach, in which beta is instead treated as a hyperparameter that is inferred from the data alongside the original parameters of the problem, and then marginalised over to obtain the final inference. We show through numerical examples that this Bayesian PR (BPR) method provides a very robust, self-adapting and computationally efficient `hands-off' solution to the problem of unrepresentative priors in Bayesian inference using NS. Moreover, unlike the original PR method, we show that even for representative priors BPR has a negligible computational overhead relative to standard nesting sampling, which suggests that it should be used as the default in all NS analyses.},
  pubstate = {prepublished},
  keywords = {Astrophysics - Instrumentation and Methods for Astrophysics,Computer Science - Neural and Evolutionary Computing,Statistics - Computation},
  file = {/home/jacopo/Zotero/storage/XH4EBV49/Chen et al. - 2022 - Bayesian posterior repartitioning for nested sampl.pdf;/home/jacopo/Zotero/storage/HPVD7B8D/1908.html}
}

@article{chopinPropertiesNestedSampling2010,
  title = {Properties of Nested Sampling},
  author = {Chopin, Nicolas and Robert, Christian P.},
  date = {2010-09-01},
  journaltitle = {Biometrika},
  shortjournal = {Biometrika},
  volume = {97},
  number = {3},
  pages = {741--755},
  issn = {0006-3444},
  doi = {10.1093/biomet/asq021},
  url = {https://doi.org/10.1093/biomet/asq021},
  urldate = {2024-11-25},
  abstract = {Nested sampling is a simulation method for approximating marginal likelihoods. We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is asymptotically Gaussian. It is shown that the asymptotic variance of the nested sampling approximation typically grows linearly with the dimension of the parameter. We discuss the applicability and efficiency of nested sampling in realistic problems, and compare it with two current methods for computing marginal likelihood. Finally, we propose an extension that avoids resorting to Markov chain Monte Carlo simulation to obtain the simulated points.},
  file = {/home/jacopo/Zotero/storage/WTVSHENE/Chopin and Robert - 2010 - Properties of nested sampling.pdf;/home/jacopo/Zotero/storage/U8BAXHJE/243485.html}
}

@book{coverElementsInformationTheory2006,
  title = {Elements of {{Information Theory}} 2nd {{Edition}}},
  author = {Cover, Thomas M. and Thomas, Joy A.},
  date = {2006-07-18},
  edition = {2nd edition},
  publisher = {Wiley-Interscience},
  location = {Hoboken, N.J},
  abstract = {The latest edition of this classic is updated with new problem sets and material   The Second Edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory.  All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points.  The Second Edition features: * Chapters reorganized to improve teaching * 200 new problems * New material on source coding, portfolio theory, and feedback capacity * Updated references  Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications.},
  isbn = {978-0-471-24195-9},
  langid = {english},
  pagetotal = {784}
}

@online{daxGroupEquivariantNeural2023,
  title = {Group Equivariant Neural Posterior Estimation},
  author = {Dax, Maximilian and Green, Stephen R. and Gair, Jonathan and Deistler, Michael and Schölkopf, Bernhard and Macke, Jakob H.},
  date = {2023-05-30},
  eprint = {2111.13139},
  eprinttype = {arXiv},
  eprintclass = {cs},
  doi = {10.48550/arXiv.2111.13139},
  url = {http://arxiv.org/abs/2111.13139},
  urldate = {2025-02-13},
  abstract = {Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.},
  pubstate = {prepublished},
  keywords = {Astrophysics - Instrumentation and Methods for Astrophysics,Computer Science - Machine Learning,General Relativity and Quantum Cosmology,Statistics - Machine Learning},
  file = {/home/jacopo/Zotero/storage/2LQESRQM/Dax et al. - 2023 - Group equivariant neural posterior estimation.pdf}
}

@online{daxNeuralImportanceSampling2022,
  title = {Neural {{Importance Sampling}} for {{Rapid}} and {{Reliable Gravitational-Wave Inference}}},
  author = {Dax, Maximilian and Green, Stephen R. and Gair, Jonathan and Pürrer, Michael and Wildberger, Jonas and Macke, Jakob H. and Buonanno, Alessandra and Schölkopf, Bernhard},
  date = {2022-10-11},
  eprint = {2210.05686},
  eprinttype = {arXiv},
  eprintclass = {astro-ph, physics:gr-qc},
  url = {http://arxiv.org/abs/2210.05686},
  urldate = {2022-11-14},
  abstract = {We combine amortized neural posterior estimation with importance sampling for fast and accurate gravitational-wave inference. We first generate a rapid proposal for the Bayesian posterior using neural networks, and then attach importance weights based on the underlying likelihood and prior. This provides (1) a corrected posterior free from network inaccuracies, (2) a performance diagnostic (the sample efficiency) for assessing the proposal and identifying failure cases, and (3) an unbiased estimate of the Bayesian evidence. By establishing this independent verification and correction mechanism we address some of the most frequent criticisms against deep learning for scientific inference. We carry out a large study analyzing 42 binary black hole mergers observed by LIGO and Virgo with the SEOBNRv4PHM and IMRPhenomXPHM waveform models. This shows a median sample efficiency of \$\textbackslash approx 10\textbackslash\%\$ (two orders-of-magnitude better than standard samplers) as well as a ten-fold reduction in the statistical uncertainty in the log evidence. Given these advantages, we expect a significant impact on gravitational-wave inference, and for this approach to serve as a paradigm for harnessing deep learning methods in scientific applications.},
  pubstate = {prepublished},
  keywords = {Astrophysics - Instrumentation and Methods for Astrophysics,Computer Science - Machine Learning,General Relativity and Quantum Cosmology,To read},
  file = {/home/jacopo/Zotero/storage/S6CAQHVF/Dax et al. - 2022 - Neural Importance Sampling for Rapid and Reliable .pdf;/home/jacopo/Zotero/storage/3P64L2AM/2210.html}
}

@online{edwardsBayesianSemiparametricPower2015,
  title = {Bayesian Semiparametric Power Spectral Density Estimation with Applications in Gravitational Wave Data Analysis},
  author = {Edwards, Matthew C. and Meyer, Renate and Christensen, Nelson},
  date = {2015-08-18},
  eprint = {1506.00185},
  eprinttype = {arXiv},
  doi = {10.48550/arXiv.1506.00185},
  url = {http://arxiv.org/abs/1506.00185},
  urldate = {2024-10-28},
  abstract = {The standard noise model in gravitational wave (GW) data analysis assumes detector noise is stationary and Gaussian distributed, with a known power spectral density (PSD) that is usually estimated using clean off-source data. Real GW data often depart from these assumptions, and misspecified parametric models of the PSD could result in misleading inferences. We propose a Bayesian semiparametric approach to improve this. We use a nonparametric Bernstein polynomial prior on the PSD, with weights attained via a Dirichlet process distribution, and update this using the Whittle likelihood. Posterior samples are obtained using a blocked Metropolis-within-Gibbs sampler. We simultaneously estimate the reconstruction parameters of a rotating core collapse supernova GW burst that has been embedded in simulated Advanced LIGO noise. We also discuss an approach to deal with non-stationary data by breaking longer data streams into smaller and locally stationary components.},
  pubstate = {prepublished},
  keywords = {General Relativity and Quantum Cosmology,Physics - Data Analysis Statistics and Probability,Statistics - Applications},
  file = {/home/jacopo/Zotero/storage/CSSEM5ZP/Edwards et al. - 2015 - Bayesian semiparametric power spectral density est.pdf;/home/jacopo/Zotero/storage/72L8T3FU/1506.html}
}

@online{handleyPolyChordNestedSampling2015,
  title = {{{PolyChord}}: Nested Sampling for Cosmology},
  shorttitle = {{{PolyChord}}},
  author = {Handley, W. J. and Hobson, M. P. and Lasenby, A. N.},
  date = {2015-03-28},
  eprint = {1502.01856},
  eprinttype = {arXiv},
  doi = {10.48550/arXiv.1502.01856},
  url = {http://arxiv.org/abs/1502.01856},
  urldate = {2024-11-22},
  abstract = {PolyChord is a novel nested sampling algorithm tailored for high dimensional parameter spaces. In addition, it can fully exploit a hierarchy of parameter speeds such as is found in CosmoMC and CAMB. It utilises slice sampling at each iteration to sample within the hard likelihood constraint of nested sampling. It can identify and evolve separate modes of a posterior semi-independently and is parallelised using openMPI. PolyChord is available for download at: http://ccpforge.cse.rl.ac.uk/gf/project/polychord/},
  pubstate = {prepublished},
  keywords = {Astrophysics - Cosmology and Nongalactic Astrophysics,Astrophysics - Instrumentation and Methods for Astrophysics},
  file = {/home/jacopo/Zotero/storage/SHRKM2XY/Handley et al. - 2015 - PolyChord nested sampling for cosmology.pdf;/home/jacopo/Zotero/storage/NEKBUEIP/1502.html}
}

@article{higsonDynamicNestedSampling2019,
  title = {Dynamic Nested Sampling: An Improved Algorithm for Parameter Estimation and Evidence Calculation},
  shorttitle = {Dynamic Nested Sampling},
  author = {Higson, Edward and Handley, Will and Hobson, Michael and Lasenby, Anthony},
  date = {2019-09-01},
  journaltitle = {Statistics and Computing},
  shortjournal = {Stat Comput},
  volume = {29},
  number = {5},
  pages = {891--913},
  issn = {1573-1375},
  doi = {10.1007/s11222-018-9844-0},
  url = {https://doi.org/10.1007/s11222-018-9844-0},
  urldate = {2024-11-25},
  abstract = {We introduce dynamic nested sampling: a generalisation of the nested sampling algorithm in which the number of “live points” varies to allocate samples more efficiently. In empirical tests the new method significantly improves calculation accuracy compared to standard nested sampling with the same number of samples; this increase in accuracy is equivalent to speeding up the computation by factors of up to \$\$\textbackslash sim 72\$\$for parameter estimation and \$\$\textbackslash sim 7\$\$for evidence calculations. We also show that the accuracy of both parameter estimation and evidence calculations can be improved simultaneously. In addition, unlike in standard nested sampling, more accurate results can be obtained by continuing the calculation for longer. Popular standard nested sampling implementations can be easily adapted to perform dynamic nested sampling, and several dynamic nested sampling software packages are now publicly available.},
  langid = {english},
  keywords = {Artificial Intelligence,Bayesian computation,Bayesian evidence,Nested sampling,Parameter estimation},
  file = {/home/jacopo/Zotero/storage/IZTV2S4F/Higson et al. - 2019 - Dynamic nested sampling an improved algorithm for.pdf}
}

@online{huCostsBayesianParameter2024,
  title = {Costs of {{Bayesian Parameter Estimation}} in {{Third-Generation Gravitational Wave Detectors}}: A {{Review}} of {{Acceleration Methods}}},
  shorttitle = {Costs of {{Bayesian Parameter Estimation}} in {{Third-Generation Gravitational Wave Detectors}}},
  author = {Hu, Qian and Veitch, John},
  date = {2024-12-03},
  eprint = {2412.02651},
  eprinttype = {arXiv},
  eprintclass = {gr-qc},
  doi = {10.48550/arXiv.2412.02651},
  url = {http://arxiv.org/abs/2412.02651},
  urldate = {2025-02-21},
  abstract = {Bayesian inference with stochastic sampling has been widely used to obtain the properties of gravitational wave (GW) sources. Although computationally intensive, its cost remains manageable for current second-generation GW detectors because of the relatively low event rate and signal-to-noise ratio (SNR). The third-generation (3G) GW detectors are expected to detect hundreds of thousands of compact binary coalescence events every year with substantially higher SNR and longer signal duration, presenting significant computational challenges. In this study, we systematically evaluate the computational costs of source parameter estimation (PE) in the 3G era by modeling the PE time cost as a function of SNR and signal duration. We examine the standard PE method alongside acceleration methods including relative binning, multibanding, and reduced order quadrature. We predict that PE for a one-month-observation catalog with 3G detectors could require billions to quadrillions of CPU core hours with the standard PE method, whereas acceleration techniques can reduce this demand to millions of core hours. These findings highlight the necessity for more efficient PE methods to enable cost-effective and environmentally sustainable data analysis for 3G detectors. In addition, we assess the accuracy of accelerated PE methods, emphasizing the need for careful treatment in high-SNR scenarios.},
  pubstate = {prepublished},
  keywords = {Astrophysics - Instrumentation and Methods for Astrophysics,General Relativity and Quantum Cosmology},
  file = {/home/jacopo/Zotero/storage/WR2D4P8V/Hu and Veitch - 2024 - Costs of Bayesian Parameter Estimation in Third-Ge.pdf;/home/jacopo/Zotero/storage/T9QJDKPY/2412.html}
}

@online{huDecodingLongdurationGravitational2024,
  title = {Decoding {{Long-duration Gravitational Waves}} from {{Binary Neutron Stars}} with {{Machine Learning}}: {{Parameter Estimation}} and {{Equations}} of {{State}}},
  shorttitle = {Decoding {{Long-duration Gravitational Waves}} from {{Binary Neutron Stars}} with {{Machine Learning}}},
  author = {Hu, Qian and Irwin, Jessica and Sun, Qi and Messenger, Christopher and Suleiman, Lami and Heng, Ik Siong and Veitch, John},
  date = {2024-12-04},
  eprint = {2412.03454},
  eprinttype = {arXiv},
  eprintclass = {gr-qc},
  doi = {10.48550/arXiv.2412.03454},
  url = {http://arxiv.org/abs/2412.03454},
  urldate = {2025-02-26},
  abstract = {Gravitational waves (GWs) from binary neutron stars (BNSs) offer valuable understanding of the nature of compact objects and hadronic matter. However, their analysis requires substantial computational resources due to the challenges in Bayesian stochastic sampling. The third-generation (3G) GW detectors are expected to detect BNS signals with significantly increased signal duration, detection rates, and signal strength, leading to a major computational burden in the 3G era. We demonstrate a machine learning-based workflow capable of producing source parameter estimation and constraints on equations of state (EOSs) for hours-long BNS signals in seconds with minimal hardware costs. We employ efficient compressions on the GW data and EOS using neural networks, based on which we build normalizing flows for inferences. Given that full Bayesian analysis is prohibitively time-intensive, we validate our model against (semi-)analytical predictions. Additionally, we estimate the computational demands of BNS signal analysis in the 3G era, showing that the machine learning methods will be crucial for future catalog-level analysis.},
  pubstate = {prepublished},
  keywords = {Astrophysics - High Energy Astrophysical Phenomena,Astrophysics - Instrumentation and Methods for Astrophysics,General Relativity and Quantum Cosmology},
  file = {/home/jacopo/Zotero/storage/MGMZFYMI/Hu et al. - 2024 - Decoding Long-duration Gravitational Waves from Bi.pdf;/home/jacopo/Zotero/storage/WIWQP7RU/2412.html}
}

@unpublished{knuthTwoNotesNotation1992,
  title = {Two Notes on Notation},
  author = {Knuth, Donald E.},
  date = {1992-04-30},
  eprint = {math/9205211},
  eprinttype = {arXiv},
  url = {http://arxiv.org/abs/math/9205211},
  urldate = {2020-03-04},
  abstract = {The author advocates two specific mathematical notations from his popular course and joint textbook, "Concrete Mathematics". The first of these, extending an idea of Iverson, is the notation "[P]" for the function which is 1 when the Boolean condition P is true and 0 otherwise. This notation can encourage and clarify the use of characteristic functions and Kronecker deltas in sums and integrals. The second notation puts Stirling numbers on the same footing as binomial coefficients. Since binomial coefficients are written on two lines in parentheses and read "n choose k", Stirling numbers of the first kind should be written on two lines in brackets and read "n cycle k", while Stirling numbers of the second kind should be written in braces and read "n subset k". (I might say "n partition k".) The written form was first suggested by Imanuel Marx. The virtues of this notation are that Stirling partition numbers frequently appear in combinatorics, and that it more clearly presents functional relations similar to those satisfied by binomial coefficients.},
  keywords = {Mathematics - History and Overview},
  file = {/home/jacopo/Zotero/storage/3UUDI7X7/Knuth - 1992 - Two notes on notation.pdf;/home/jacopo/Zotero/storage/IAG3XHLT/9205211.html}
}

@article{leslieModebymodeRelativeBinning2021,
  title = {Mode-by-Mode Relative Binning: {{Fast}} Likelihood Estimation for Gravitational Waveforms with Spin-Orbit Precession and Multiple Harmonics},
  shorttitle = {Mode-by-Mode Relative Binning},
  author = {Leslie, Nathaniel and Dai, Liang and Pratten, Geraint},
  date = {2021-12-22},
  journaltitle = {Physical Review D},
  shortjournal = {Phys. Rev. D},
  volume = {104},
  number = {12},
  pages = {123030},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.104.123030},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.104.123030},
  urldate = {2024-02-27},
  abstract = {Faster likelihood evaluation enhances the efficiency of gravitational wave signal analysis. We present mode-by-mode relative binning, a new method designed for obtaining fast and accurate likelihoods for advanced waveform models that include spin-orbit precession effects and multiple radiation harmonics from compact binary coalescence. Leveraging the “twisting-up” procedure of constructing precessing waveform modes from nonprecessing ones, the new method mitigates degrade of relative binning accuracy due to interference from superimposed modes. Additionally, we supplement algorithms for optimizing the choice of frequency bins specific to any given strain signal under analysis. Using the new method, we are able to evaluate the likelihood with up to an order of magnitude reduction in the number of waveform model calls per frequency compared to the previously used relative binning scheme, and achieve better likelihood accuracy than is sufficient for obtaining source parameter posterior distributions that are indistinguishable from the exact ones.},
  file = {/home/jacopo/Zotero/storage/CSASE3TT/Leslie et al. - 2021 - Mode-by-mode relative binning Fast likelihood est.pdf}
}

@article{littenbergBayesianInferenceSpectral2015,
  title = {Bayesian Inference for Spectral Estimation of Gravitational Wave Detector Noise},
  author = {Littenberg, Tyson B. and Cornish, Neil J.},
  date = {2015-04-14},
  journaltitle = {Physical Review D},
  shortjournal = {Phys. Rev. D},
  volume = {91},
  number = {8},
  pages = {084034},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.91.084034},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.91.084034},
  urldate = {2025-02-13},
  abstract = {Gravitational wave data from ground-based detectors is dominated by instrument noise. Signals will be comparatively weak, and our understanding of the noise will influence detection confidence and signal characterization. Mismodeled noise can produce large systematic biases in both model selection and parameter estimation. Here we introduce a multicomponent, variable dimension, parametrized model to describe the Gaussian-noise power spectrum for data from ground-based gravitational wave interferometers. Called BayesLine, the algorithm models the noise power spectral density using cubic splines for smoothly varying broadband noise and Lorentzians for narrow-band line features in the spectrum. We describe the algorithm and demonstrate its performance on data from the fifth and sixth LIGO science runs. Once fully integrated into LIGO/Virgo data analysis software, BayesLine will produce accurate spectral estimation and provide a means for marginalizing inferences drawn from the data over all plausible noise spectra.},
  file = {/home/jacopo/Zotero/storage/WCGF8KUI/Littenberg and Cornish - 2015 - Bayesian inference for spectral estimation of grav.pdf;/home/jacopo/Zotero/storage/Z263BLQ7/PhysRevD.91.html}
}

@online{morisakiRapidLocalizationInference2023,
  title = {Rapid Localization and Inference on Compact Binary Coalescences with the {{Advanced LIGO-Virgo-KAGRA}} Gravitational-Wave Detector Network},
  author = {Morisaki, Soichiro and Smith, Rory and Tsukada, Leo and Sachdev, Surabhi and Stevenson, Simon and Talbot, Colm and Zimmerman, Aaron},
  date = {2023-07-25},
  eprint = {2307.13380},
  eprinttype = {arXiv},
  eprintclass = {astro-ph, physics:gr-qc},
  url = {http://arxiv.org/abs/2307.13380},
  urldate = {2023-07-26},
  abstract = {We present a rapid parameter estimation framework for compact binary coalescence (CBC) signals observed by the LIGO-Virgo-KAGRA (LVK) detector network. The goal of our framework is to enable optimal source localization of binary neutron star (BNS) signals in low latency, as well as improve the overall scalability of full CBC parameter estimation analyses. Our framework is based on the reduced order quadrature (ROQ) technique, and resolves its shortcomings by utilizing multiple ROQ bases in a single parameter estimation run. We have also developed sets of compact ROQ bases for various waveform models, IMRPhenomD, IMRPhenomPv2, IMRPhenomPv2\$\textbackslash\_\$NRTidalv2, and IMRPhenomXPHM. We benchmark our framework with hundreds of simulated observations of BNS signals by the LIGO-Virgo detector network, and demonstrate that it provides accurate and unbiased estimates on BNS source location, with a median analysis time of \$6\$ minutes. The median searched area is reduced by around 30\$\textbackslash\%\$ compared to estimates produced by BAYESTAR: from \$21.8\textbackslash,\textbackslash mathrm\{deg\textasciicircum 2\}\$ to \$16.6\textbackslash,\textbackslash mathrm\{deg\textasciicircum 2\}\$. Our framework also enables detailed parameter estimation taking into account gravitational-wave higher multipole moments, the tidal deformation of colliding objects, and detector calibration errors of amplitude and phase with the time scale of hours. Our rapid parameter estimation technique has been implemented in one of the LVK parameter estimation engines, BILBY, and is being employed by the automated parameter estimation analysis of the LVK alert system.},
  pubstate = {prepublished},
  keywords = {Astrophysics - High Energy Astrophysical Phenomena,Astrophysics - Instrumentation and Methods for Astrophysics,General Relativity and Quantum Cosmology},
  file = {/home/jacopo/Zotero/storage/KZ2C55AA/Morisaki et al. - 2023 - Rapid localization and inference on compact binary.pdf;/home/jacopo/Zotero/storage/YXPQBBQW/2307.html}
}

@online{narolaRelativeBinningComplete2023,
  title = {Relative Binning for Complete Gravitational-Wave Parameter Estimation with Higher-Order Modes and Precession, and Applications to Lensing and Third-Generation Detectors},
  author = {Narola, Harsh and Janquart, Justin and Meijer, Quirijn and Haris, K. and Broeck, Chris Van Den},
  date = {2023-08-23},
  eprint = {2308.12140},
  eprinttype = {arXiv},
  eprintclass = {gr-qc},
  url = {http://arxiv.org/abs/2308.12140},
  urldate = {2023-08-28},
  abstract = {Once a gravitational wave signal is detected, the measurement of its source parameters is important to achieve various scientific goals. This is done through Bayesian inference, where the analysis cost increases with the model complexity and the signal duration. For typical binary black hole signals with precession and higher-order modes, one has 15 model parameters. With standard methods, such analyses require at least a few days. For strong gravitational wave lensing, where multiple images of the same signal are produced, the joint analysis of two data streams requires 19 parameters, further increasing the complexity and run time. Moreover, for third generation detectors, due to the lowered minimum sensitive frequency, the signal duration increases, leading to even longer analysis times. With the increased detection rate, such analyses can then become intractable. In this work, we present a fast and precise parameter estimation method relying on relative binning and capable of including higher-order modes and precession. We also extend the method to perform joint Bayesian inference for lensed gravitational wave signals. Then, we compare its accuracy and speed to those of state-of-the-art parameter estimation routines by analyzing a set of simulated signals for the current and third generation of interferometers. Additionally, for the first time, we analyze some real events known to contain higher-order modes with relative binning. For binary black hole systems with a total mass larger than \$50\textbackslash, M\_\{\textbackslash odot\}\$, our method is about 2.5 times faster than current techniques. This speed-up increases for lower masses, with the analysis time being reduced by a factor of 10 on average. In all cases, the recovered posterior probability distributions for the parameters match those found with traditional techniques.},
  pubstate = {prepublished},
  keywords = {General Relativity and Quantum Cosmology},
  file = {/home/jacopo/Zotero/storage/2WXHHT3L/Narola et al. - 2023 - Relative binning for complete gravitational-wave p.pdf;/home/jacopo/Zotero/storage/79W95ZMA/2308.html}
}

@online{petrosyanSuperNestAcceleratedNested2022,
  title = {{{SuperNest}}: Accelerated Nested Sampling Applied to Astrophysics and Cosmology},
  shorttitle = {{{SuperNest}}},
  author = {Petrosyan, Aleksandr and Handley, William James},
  date = {2022-12-04},
  eprint = {2212.01760},
  eprinttype = {arXiv},
  eprintclass = {astro-ph, physics:physics},
  url = {http://arxiv.org/abs/2212.01760},
  urldate = {2022-12-06},
  abstract = {We present a method for improving the performance of nested sampling as well as its accuracy. Building on previous work by Chen et al., we show that posterior repartitioning may be used to reduce the amount of time nested sampling spends in compressing from prior to posterior if a suitable ``proposal'' distribution is supplied. We showcase this on a cosmological example with a Gaussian posterior, and release the code as an LGPL licensed, extensible Python package https://gitlab.com/a-p-petrosyan/sspr.},
  pubstate = {prepublished},
  keywords = {Astrophysics - Cosmology and Nongalactic Astrophysics,Physics - Computational Physics},
  file = {/home/jacopo/Zotero/storage/YESGL27C/Petrosyan and Handley - 2022 - SuperNest accelerated nested sampling applied to .pdf;/home/jacopo/Zotero/storage/938JT4X9/2212.html}
}

@article{romero-shawWhenModelsFail2022,
  title = {When Models Fail: An Introduction to Posterior Predictive Checks and Model Misspecification in Gravitational-Wave Astronomy},
  shorttitle = {When Models Fail},
  author = {Romero-Shaw, Isobel M. and Thrane, Eric and Lasky, Paul D.},
  date = {2022},
  journaltitle = {Publications of the Astronomical Society of Australia},
  shortjournal = {Publ. Astron. Soc. Aust.},
  volume = {39},
  eprint = {2202.05479},
  eprinttype = {arXiv},
  eprintclass = {astro-ph, physics:gr-qc},
  pages = {e025},
  issn = {1323-3580, 1448-6083},
  doi = {10.1017/pasa.2022.24},
  url = {http://arxiv.org/abs/2202.05479},
  urldate = {2024-02-24},
  abstract = {Bayesian inference is a powerful tool in gravitational-wave astronomy. It enables us to deduce the properties of merging compact-object binaries and to determine how these mergers are distributed as a population according to mass, spin, and redshift. As key results are increasingly derived using Bayesian inference, there is increasing scrutiny on Bayesian methods. In this review, we discuss the phenomenon of \textbackslash textit\{model misspecification\}, in which results obtained with Bayesian inference are misleading because of deficiencies in the assumed model(s). Such deficiencies can impede our inferences of the true parameters describing physical systems. They can also reduce our ability to distinguish the "best fitting" model: it can be misleading to say that Model\textasciitilde A is preferred over Model\textasciitilde B if both models are manifestly poor descriptions of reality. Broadly speaking, there are two ways in which models fail: models that fail to adequately describe the data (either the signal or the noise) have misspecified likelihoods. Population models -- designed, for example, to describe the distribution of black hole masses -- may fail to adequately describe the true population due to a misspecified prior. We recommend tests and checks that are useful for spotting misspecified models using examples inspired by gravitational-wave astronomy. We include companion python notebooks to illustrate essential concepts.},
  keywords = {Astrophysics - Instrumentation and Methods for Astrophysics,General Relativity and Quantum Cosmology},
  file = {/home/jacopo/Zotero/storage/L3ZGVXBH/Romero-Shaw et al. - 2022 - When models fail an introduction to posterior pre.pdf;/home/jacopo/Zotero/storage/7VW2EV8L/2202.html}
}

@online{rouletInferringBinaryProperties2024,
  title = {Inferring {{Binary Properties}} from {{Gravitational Wave Signals}}},
  author = {Roulet, Javier and Venumadhav, Tejaswi},
  date = {2024-02-17},
  eprint = {2402.11439},
  eprinttype = {arXiv},
  eprintclass = {astro-ph, physics:gr-qc},
  doi = {10.1146/annurev-nucl-121423-100725},
  url = {http://arxiv.org/abs/2402.11439},
  urldate = {2024-02-20},
  abstract = {This review provides a conceptual and technical survey of methods for parameter estimation of gravitational wave signals in ground-based interferometers such as LIGO and Virgo. We introduce the framework of Bayesian inference and provide an overview of models for the generation and detection of gravitational waves from compact binary mergers, focusing on the essential features that are observable in the signals. Within the traditional likelihood-based paradigm, we describe various approaches for enhancing the efficiency and robustness of parameter inference. This includes techniques for accelerating likelihood evaluations, such as heterodyne/relative binning, reduced-order quadrature, multibanding and interpolation. We also cover methods to simplify the analysis to improve convergence, via reparametrization, importance sampling and marginalization. We end with a discussion of recent developments in the application of likelihood-free (simulation-based) inference methods to gravitational wave data analysis.},
  pubstate = {prepublished},
  keywords = {Astrophysics - High Energy Astrophysical Phenomena,General Relativity and Quantum Cosmology},
  file = {/home/jacopo/Zotero/storage/9HIFFZMH/Roulet and Venumadhav - 2024 - Inferring Binary Properties from Gravitational Wav.pdf;/home/jacopo/Zotero/storage/9QZTGYEB/2402.html}
}

@online{rouletRemovingDegeneracyMultimodality2022,
  title = {Removing Degeneracy and Multimodality in Gravitational Wave Source Parameters},
  author = {Roulet, Javier and Olsen, Seth and Mushkin, Jonathan and Islam, Tousif and Venumadhav, Tejaswi and Zackay, Barak and Zaldarriaga, Matias},
  date = {2022-07-07},
  eprint = {2207.03508},
  eprinttype = {arXiv},
  eprintclass = {astro-ph, physics:gr-qc},
  doi = {10.48550/arXiv.2207.03508},
  url = {http://arxiv.org/abs/2207.03508},
  urldate = {2022-07-11},
  abstract = {Quasicircular binary black hole mergers are described by 15 parameters, of which gravitational wave observations can typically constrain only \$\textbackslash sim 10\$ independent combinations to varying degree. In this work, we devise coordinates that remove correlations, and disentangle well- and poorly-measured quantities. Additionally, we identify approximate discrete symmetries in the posterior as the primary cause of multimodality, and design a method to tackle this type of multimodality. The resulting posteriors have little structure and can be sampled efficiently and robustly. We provide a Python package for parameter estimation, cogwheel, that implements these methods together with other algorithms for accelerating the inference process. One of the coordinates we introduce is a spin azimuth that can be measured remarkably well in the presence of orbital precession, and we anticipate that this will shed light on the occurrence of spin-orbit misalignment in nature.},
  pubstate = {prepublished},
  keywords = {Astrophysics - High Energy Astrophysical Phenomena,Astrophysics - Instrumentation and Methods for Astrophysics,General Relativity and Quantum Cosmology},
  file = {/home/jacopo/Zotero/storage/BRZI6AS4/Roulet et al. - 2022 - Removing degeneracy and multimodality in gravitati.pdf;/home/jacopo/Zotero/storage/67HNEUK8/2207.html}
}

@online{salehTemperedMultifidelityImportance2024,
  title = {Tempered {{Multifidelity Importance Sampling}} for {{Gravitational Wave Parameter Estimation}}},
  author = {Saleh, Bassel and Zimmerman, Aaron and Chen, Peng and Ghattas, Omar},
  date = {2024-05-29},
  eprint = {2405.19407},
  eprinttype = {arXiv},
  eprintclass = {astro-ph, physics:gr-qc, stat},
  url = {http://arxiv.org/abs/2405.19407},
  urldate = {2024-05-31},
  abstract = {Estimating the parameters of compact binaries which coalesce and produce gravitational waves is a challenging Bayesian inverse problem. Gravitational-wave parameter estimation lies within the class of multifidelity problems, where a variety of models with differing assumptions, levels of fidelity, and computational cost are available for use in inference. In an effort to accelerate the solution of a Bayesian inverse problem, cheaper surrogates for the best models may be used to reduce the cost of likelihood evaluations when sampling the posterior. Importance sampling can then be used to reweight these samples to represent the true target posterior, incurring a reduction in the effective sample size. In cases when the problem is high dimensional, or when the surrogate model produces a poor approximation of the true posterior, this reduction in effective samples can be dramatic and render multifidelity importance sampling ineffective. We propose a novel method of tempered multifidelity importance sampling in order to remedy this issue. With this method the biasing distribution produced by the low-fidelity model is tempered, allowing for potentially better overlap with the target distribution. There is an optimal temperature which maximizes the efficiency in this setting, and we propose a low-cost strategy for approximating this optimal temperature using samples from the untempered distribution. In this paper, we motivate this method by applying it to Gaussian target and biasing distributions. Finally, we apply it to a series of problems in gravitational wave parameter estimation and demonstrate improved efficiencies when applying the method to real gravitational wave detections.},
  langid = {english},
  pubstate = {prepublished},
  keywords = {Astrophysics - Instrumentation and Methods for Astrophysics,General Relativity and Quantum Cosmology,Statistics - Methodology},
  file = {/home/jacopo/Zotero/storage/KYS2DLWW/Saleh et al. - 2024 - Tempered Multifidelity Importance Sampling for Gra.pdf}
}

@book{siviaDataAnalysisBayesian2006,
  title = {Data {{Analysis}}: {{A Bayesian Tutorial}}},
  shorttitle = {Data {{Analysis}}},
  author = {Sivia, Devinderjit and Skilling, John},
  date = {2006-06},
  eprint = {lYMSDAAAQBAJ},
  eprinttype = {googlebooks},
  publisher = {Oxford University Press},
  abstract = {Statistics lectures have been a source of much bewilderment and frustration for generations of students. This book attempts to remedy the situation by expounding a logical and unified approach to the whole subject of data analysis.  This text is intended as a tutorial guide for senior undergraduates and research students in science and engineering. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to image processing. Other topics covered include reliability analysis, multivariate optimization, least-squares and maximum likelihood, error-propagation, hypothesis testing, maximum entropy and experimental design.  The Second Edition of this successful tutorial book contains a new chapter on extensions to the ubiquitous least-squares procedure, allowing for the straightforward handling of outliers and unknown correlated noise, and a cutting-edge contribution from John Skilling on a novel numerical technique for Bayesian computation called 'nested sampling'.},
  isbn = {978-0-19-856831-5},
  langid = {english},
  pagetotal = {259},
  keywords = {Mathematics / Applied,Mathematics / Probability & Statistics / Bayesian Analysis,Mathematics / Probability & Statistics / General,Science / Physics / General},
  file = {/home/jacopo/Zotero/storage/FPF4636S/Sivia and Skilling - 2006 - Data Analysis A Bayesian Tutorial.pdf}
}

@inproceedings{skillingNestedSampling2004,
  title = {Nested {{Sampling}}},
  booktitle = {{{AIP Conference Proceedings}}},
  author = {Skilling, John},
  date = {2004},
  volume = {735},
  pages = {395--405},
  publisher = {AIP},
  location = {Garching (Germany)},
  issn = {0094243X},
  doi = {10.1063/1.1835238},
  url = {https://pubs.aip.org/aip/acp/article/735/1/395-405/748716},
  urldate = {2024-11-25},
  abstract = {The evidence Z is often the single most important number in the [Bayesian] problem and I think every effort should be devoted to calculating it” (MacKay 2003)[1]. Nested sampling does this by giving a direct estimate of the density of states. Posterior samples are an optional byproduct.},
  eventtitle = {{{BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING}}: 24th {{International Workshop}} on {{Bayesian Inference}} and {{Maximum Entropy Methods}} in {{Science}} and {{Engineering}}},
  langid = {english},
  file = {/home/jacopo/Zotero/storage/3WGY3HK7/Skilling - 2004 - Nested Sampling.pdf}
}

@article{skillingNestedSamplingGeneral2006,
  title = {Nested Sampling for General {{Bayesian}} Computation},
  author = {Skilling, John},
  date = {2006-12},
  journaltitle = {Bayesian Analysis},
  volume = {1},
  number = {4},
  pages = {833--859},
  publisher = {International Society for Bayesian Analysis},
  issn = {1936-0975, 1931-6690},
  doi = {10.1214/06-BA127},
  url = {https://projecteuclid.org/journals/bayesian-analysis/volume-1/issue-4/Nested-sampling-for-general-Bayesian-computation/10.1214/06-BA127.full},
  urldate = {2021-09-15},
  abstract = {Nested sampling estimates directly how the likelihood function relates to prior mass. The evidence (alternatively the marginal likelihood, marginal density of the data, or the prior predictive) is immediately obtained by summation. It is the prime result of the computation, and is accompanied by an estimate of numerical uncertainty. Samples from the posterior distribution are an optional by-product, obtainable for any temperature. The method relies on sampling within a hard constraint on likelihood value, as opposed to the softened likelihood of annealing methods. Progress depends only on the shape of the "nested" contours of likelihood, and not on the likelihood values. This invariance (over monotonic re-labelling) allows the method to deal with a class of phase-change problems which effectively defeat thermal annealing.},
  keywords = {algorithm,annealing,Bayesian computation,evidence,marginal likelihood,Model selection,nest,phase change},
  file = {/home/jacopo/Zotero/storage/B9ADWEC4/Skilling_2006_Nested sampling for general Bayesian computation.pdf;/home/jacopo/Zotero/storage/6BEH25TG/06-BA127.html}
}

@article{smithBayesianInferenceGravitational2021,
  title = {Bayesian Inference for Gravitational Waves from Binary Neutron Star Mergers in Third-Generation Observatories},
  author = {Smith, Rory and Borhanian, Ssohrab and Sathyaprakash, Bangalore and Vivanco, Francisco Hernandez and Field, Scott and Lasky, Paul and Mandel, Ilya and Morisaki, Soichiro and Ottaway, David and Slagmolen, Bram and Thrane, Eric and Töyrä, Daniel and Vitale, Salvatore},
  date = {2021-08-20},
  journaltitle = {Physical Review Letters},
  shortjournal = {Phys. Rev. Lett.},
  volume = {127},
  number = {8},
  eprint = {2103.12274},
  eprinttype = {arXiv},
  eprintclass = {gr-qc},
  pages = {081102},
  issn = {0031-9007, 1079-7114},
  doi = {10.1103/PhysRevLett.127.081102},
  url = {http://arxiv.org/abs/2103.12274},
  urldate = {2025-02-27},
  abstract = {Third-generation (3G) gravitational-wave detectors will observe thousands of coalescing neutron star binaries with unprecedented fidelity. Extracting the highest precision science from these signals is expected to be challenging owing to both high signal-to-noise ratios and long-duration signals. We demonstrate that current Bayesian inference paradigms can be extended to the analysis of binary neutron star signals without breaking the computational bank. We construct reduced order models for \$\textbackslash sim 90\textbackslash,\textbackslash mathrm\{minute\}\$ long gravitational-wave signals, covering the observing band (\$5-2048\textbackslash,\textbackslash mathrm\{Hz\}\$), speeding up inference by a factor of \$\textbackslash sim 1.3\textbackslash times 10\textasciicircum 4\$ compared to the calculation times without reduced order models. The reduced order models incorporate key physics including the effects of tidal deformability, amplitude modulation due to the Earth's rotation, and spin-induced orbital precession. We show how reduced order modeling can accelerate inference on data containing multiple, overlapping gravitational-wave signals, and determine the speedup as a function of the number of overlapping signals. Thus, we conclude that Bayesian inference is computationally tractable for the long-lived, overlapping, high signal-to-noise-ratio events present in 3G observatories.},
  keywords = {Astrophysics - High Energy Astrophysical Phenomena,Astrophysics - Instrumentation and Methods for Astrophysics,General Relativity and Quantum Cosmology},
  file = {/home/jacopo/Zotero/storage/TYVI87AJ/Smith et al. - 2021 - Bayesian inference for gravitational waves from bi.pdf;/home/jacopo/Zotero/storage/6RM5HHLV/2103.html}
}

@article{speagleDYNESTYDynamicNested2020,
  title = {{{DYNESTY}}: A Dynamic Nested Sampling Package for Estimating {{Bayesian}} Posteriors and Evidences},
  shorttitle = {{{DYNESTY}}},
  author = {Speagle, Joshua S.},
  date = {2020-04-01},
  journaltitle = {Monthly Notices of the Royal Astronomical Society},
  volume = {493},
  pages = {3132--3158},
  publisher = {OUP},
  issn = {0035-8711},
  doi = {10.1093/mnras/staa278},
  url = {https://ui.adsabs.harvard.edu/abs/2020MNRAS.493.3132S},
  urldate = {2024-11-22},
  abstract = {We present DYNESTY, a public, open-source, PYTHON package to estimate Bayesian posteriors and evidences (marginal likelihoods) using the dynamic nested sampling methods developed by Higson et al. By adaptively allocating samples based on posterior structure, dynamic nested sampling has the benefits of Markov chain Monte Carlo (MCMC) algorithms that focus exclusively on posterior estimation while retaining nested sampling's ability to estimate evidences and sample from complex, multimodal distributions. We provide an overview of nested sampling, its extension to dynamic nested sampling, the algorithmic challenges involved, and the various approaches taken to solve them in this and previous work. We then examine DYNESTY's performance on a variety of toy problems along with several astronomical applications. We find in particular problems DYNESTY can provide substantial improvements in sampling efficiency compared to popular MCMC approaches in the astronomical literature. More detailed statistical results related to nested sampling are also included in the appendix.},
  keywords = {Astrophysics - Instrumentation and Methods for Astrophysics,methods: data analysis,methods: statistical,Statistics - Computation},
  annotation = {ADS Bibcode: 2020MNRAS.493.3132S},
  file = {/home/jacopo/Zotero/storage/FGFU7D67/Speagle - 2020 - DYNESTY a dynamic nested sampling package for est.pdf}
}

@article{tissinoCombiningEffectiveonebodyAccuracy2023,
  title = {Combining Effective-One-Body Accuracy and Reduced-Order-Quadrature Speed for Binary Neutron Star Merger Parameter Estimation with Machine Learning},
  author = {Tissino, Jacopo and Carullo, Gregorio and Breschi, Matteo and Gamba, Rossella and Schmidt, Stefano and Bernuzzi, Sebastiano},
  date = {2023},
  journaltitle = {Phys. Rev. D},
  volume = {107},
  number = {8},
  eprint = {2210.15684},
  eprinttype = {arXiv},
  eprintclass = {gr-qc},
  pages = {084037},
  doi = {https://journals.aps.org/prd/abstract/10.1103/PhysRevD.107.084037},
  url = {http://arxiv.org/abs/2210.15684},
  urldate = {2022-11-04},
  abstract = {We present mlgw-bns, a gravitational waveform surrogate that allows for a significant improvement in the generation speed of frequency-domain waveforms for binary neutron star mergers, at a negligible cost in accuracy. This improvement is achieved by training a machine-learning model on a dataset of waveforms generated with an accurate but comparatively costlier approximant: the state-of-the-art effective-one-body model TEOBResumSPA. When coupled to a reduced-order scheme, mlgw-bns can accelerate waveform generation up to a factor of \textasciitilde 35. By analyzing GW170817 in realistic parameter estimation settings with our scheme, we showcase an overall speedup against TEOBResumSPA greater than an order of magnitude. Our methodology will bear its largest impact by allowing routine usage of accurate effective-one-body models with next-generation detectors.},
  keywords = {General Relativity and Quantum Cosmology},
  file = {/home/jacopo/Zotero/storage/6F5XJJH2/Tissino et al. - 2022 - Combining effective-one-body accuracy and reduced-.pdf;/home/jacopo/Zotero/storage/QU2ZFHGX/2210.html}
}

@article{whittleCurvePeriodogramSmoothing1957,
  title = {Curve and {{Periodogram Smoothing}}},
  author = {Whittle, P.},
  date = {1957-01-01},
  journaltitle = {Journal of the Royal Statistical Society Series B: Statistical Methodology},
  volume = {19},
  number = {1},
  pages = {38--47},
  issn = {1369-7412, 1467-9868},
  doi = {10.1111/j.2517-6161.1957.tb00242.x},
  url = {https://academic.oup.com/jrsssb/article/19/1/38/7026758},
  urldate = {2025-02-11},
  abstract = {Summary             The difficulty in constructing smoothing formulae is to express quantitatively the type of smoothness one expects of the curve one is estimating. An argument is given in Sections 1 and 3 for formulating this “smoothness hypothesis” in terms of the properties of a population of curves of which the curve being estimated is a member. In equation (20) we obtain a solution for the matrix of optimum weighting coefficients in terms of certain “population moments” of the ordinates of the curve. Explicit formulae based on special assumptions are deduced in equations (34), (56)–(58). General information is gained on the way the optimum smoothing function and the variance of the smoothed estimate vary with the sample size and with the assumed degree of smoothness of the parent curve.},
  langid = {english},
  file = {/home/jacopo/Zotero/storage/JQY44Z36/Whittle - 1957 - Curve and Periodogram Smoothing.pdf}
}

@online{williamsImportanceNestedSampling2023,
  title = {Importance Nested Sampling with Normalising Flows},
  author = {Williams, Michael J. and Veitch, John and Messenger, Chris},
  date = {2023-02-16},
  eprint = {2302.08526},
  eprinttype = {arXiv},
  eprintclass = {astro-ph, physics:gr-qc},
  doi = {10.48550/arXiv.2302.08526},
  url = {http://arxiv.org/abs/2302.08526},
  urldate = {2023-02-21},
  abstract = {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 2.64 and 12.96 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 33 minutes, whilst only requiring \$1.05\textbackslash times10\textasciicircum 6\$ likelihood evaluations compared to \$1.42\textbackslash times10\textasciicircum 6\$ for nessai and \$4.30\textbackslash times10\textasciicircum 7\$ for dynesty. These results demonstrate the i-nessai is consistent with nessai and dynesty whilst also being more efficient.},
  pubstate = {prepublished},
  keywords = {Astrophysics - High Energy Astrophysical Phenomena,Astrophysics - Instrumentation and Methods for Astrophysics,General Relativity and Quantum Cosmology},
  file = {/home/jacopo/Zotero/storage/UTCGC9YD/Williams et al. - 2023 - Importance nested sampling with normalising flows.pdf;/home/jacopo/Zotero/storage/TVAPZSUH/2302.html}
}

@unpublished{zackayRelativeBinningFast2018,
  title = {Relative {{Binning}} and {{Fast Likelihood Evaluation}} for {{Gravitational Wave Parameter Estimation}}},
  author = {Zackay, Barak and Dai, Liang and Venumadhav, Tejaswi},
  date = {2018-08-02},
  eprint = {1806.08792},
  eprinttype = {arXiv},
  eprintclass = {astro-ph, physics:gr-qc},
  url = {http://arxiv.org/abs/1806.08792},
  urldate = {2021-09-14},
  abstract = {We present a method to accelerate the evaluation of the likelihood in gravitational wave parameter estimation. Parameter estimation codes compute likelihoods of similar waveforms, whose phases and amplitudes differ smoothly with frequency. We exploit this by precomputing frequency-binned overlaps of the best-fit waveform with the data. We show how these summary data can be used to approximate the likelihood of any waveform that is sufficiently probable within the required accuracy. We demonstrate that \$\textbackslash simeq 60\$ bins suffice to accurately compute likelihoods for strain data at a sampling rate of \$4096\textbackslash,\$Hz and duration of \$T=2048\textbackslash,\$s around the binary neutron star merger GW170817. Relative binning speeds up parameter estimation for frequency domain waveform models by a factor of \$\textbackslash sim 10\textasciicircum 4\$ compared to naive matched filtering and \$\textbackslash sim 10\$ compared to reduced order quadrature.},
  keywords = {Astrophysics - Instrumentation and Methods for Astrophysics,General Relativity and Quantum Cosmology,To read},
  file = {/home/jacopo/Zotero/storage/V3JZZWST/Zackay et al_2018_Relative Binning and Fast Likelihood Evaluation for Gravitational Wave.pdf;/home/jacopo/Zotero/storage/64QK56C5/1806.html}
}