The NANOGrav 15-year Gravitational-Wave Background Methods

Abstract

Pulsar timing arrays (PTAs) use an array of millisecond pulsars to search for gravitational waves in the nanohertz regime in pulse time of arrival data. This paper presents rigorous tests of PTA methods, examining their consistency across the relevant parameter space. We discuss updates to the 15-year isotropic gravitational-wave background analyses and their corresponding code representations. Descriptions of the internal structure of the flagship algorithms Enterprise and PTMCMCSampler are given to facilitate understanding of the PTA likelihood structure, how models are built, and what methods are currently used in sampling the high-dimensional PTA parameter space. We introduce a novel version of the PTA likelihood that uses a two-step marginalization procedure that performs much faster in gravitational wave searches, reducing the required resources facilitating the computation of Bayes factors via thermodynamic integration and sampling a large number of realizations for computing Bayesian false-alarm probabilities. We perform stringent tests of consistency and correctness of the Bayesian and frequentist analysis methods. For the Bayesian analysis, we test prior recovery, simulation recovery, and Bayes factors. For the frequentist analysis, we test that the optimal statistic, when modified to account for a non-negligible gravitational-wave background, accurately recovers the amplitude of the background. We also summarize recent advances and tests performed on the optimal statistic in the literature from both GWB detection and parameter estimation perspectives. The tests presented here validate current analyses of PTA data.

30 pages, 10 figures, 1 table; Companion paper to "The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background"; For questions or comments, please email [email protected]; updated to journal version

References in corpus (54)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• Observation of Gravitational Waves from a Binary Black Hole Merger
• GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run
• Rank-normalization, folding, and localization: An improved $\hat{R}$ for assessing convergence of MCMC
• The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
• The NANOGrav 15-year Data Set: Search for Signals from New Physics
• The NANOGrav 12.5-year Data Set: Search For An Isotropic Stochastic Gravitational-Wave Background
• The NANOGrav 11-year Data Set: High-precision timing of 45 Millisecond Pulsars
• The Parkes Pulsar Timing Array Project
• High-precision timing of 42 millisecond pulsars with the European Pulsar Timing Array
• The North American Nanohertz Observatory for Gravitational Waves
• BayesWave: Bayesian Inference for Gravitational Wave Bursts and Instrument Glitches
• The NANOGrav 11-year Data Set: Pulsar-timing Constraints On The Stochastic Gravitational-wave Background
• The NANOGrav 15-year Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational Wave Background
• The NANOGrav 15-year Data Set: Observations and Timing of 68 Millisecond Pulsars
• The International Pulsar Timing Array second data release: Search for an isotropic Gravitational Wave Background
• On the evidence for a common-spectrum process in the search for the nanohertz gravitational-wave background with the Parkes Pulsar Timing Array
• Dynamic temperature selection for parallel-tempering in Markov chain Monte Carlo simulations
• The International Pulsar Timing Array: Second data release
• The Astrophysics of Nanohertz Gravitational Waves
• Common-red-signal analysis with 24-yr high-precision timing of the European Pulsar Timing Array: Inferences in the stochastic gravitational-wave background search
• Assessing the Role of Spin Noise in the Precision Timing of Millisecond Pulsars
• Optimal strategies for gravitational wave stochastic background searches in pulsar timing data
• On measuring the gravitational-wave background using Pulsar Timing Arrays
• PINT: A Modern Software Package for Pulsar Timing
• The NANOGrav 11-Year Data Set: Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries
• The NANOGrav 15-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries
• The NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget
• Dispersion Measure Variations and their Effect on Precision Pulsar Timing
• NANOGrav Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries in Circular Orbits
• Hyper-efficient model-independent Bayesian method for the analysis of pulsar timing data
• A study of spatial correlations in pulsar timing array data
• New advances in the Gaussian-process approach to pulsar-timing data analysis
• Nested Sampling Methods
• Time-domain Implementation of the Optimal Cross-Correlation Statistic for Stochastic Gravitational-Wave Background Searches in Pulsar Timing Data
• Modeling the uncertainties of solar-system ephemerides for robust gravitational-wave searches with pulsar timing arrays
• All correlations must die: Assessing the significance of a stochastic gravitational-wave background in pulsar-timing arrays
• Bilby-MCMC: An MCMC sampler for gravitational-wave inference
• The MeerTime Pulsar Timing Array -- A Census of Emission Properties and Timing Potential
• Towards Robust Gravitational Wave Detection with Pulsar Timing Arrays
• Noise-marginalized optimal statistic: A robust hybrid frequentist-Bayesian statistic for the stochastic gravitational-wave background in pulsar timing arrays
• Hellings and Downs correlation of an arbitrary set of pulsars
• The NANOGrav 12.5-year data set: Search for Non-Einsteinian Polarization Modes in theGravitational-Wave Background
• Low-rank approximations for large stationary covariance matrices, as used in the Bayesian and generalized-least-squares analysis of pulsar-timing data
• Accurate characterization of the stochastic gravitational-wave background with pulsar timing arrays by likelihood reweighting
• Evaluating the prevalence of spurious correlations in pulsar timing array datasets
• Consistency of the Parkes Pulsar Timing Array Signal with a Nanohertz Gravitational-wave Background
• Generalized optimal statistic for characterizing multiple correlated signals in pulsar timing arrays
• Toward robust detections of nanohertz gravitational waves
• Posterior predictive checking for gravitational-wave detection with pulsar timing arrays: I. The optimal statistic
• Exploring the Capabilities of Gibbs Sampling in Pulsar Timing Arrays
• Efficient Gravitational Wave Searches with Pulsar Timing Arrays using Hamiltonian Monte Carlo
• Robust parameter estimation from pulsar timing data

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