New advances in the Gaussian-process approach to pulsar-timing data analysis

Abstract

In this work we review the application of the theory of Gaussian processes to the modeling of noise in pulsar-timing data analysis, and we derive various useful and optimized representations for the likelihood expressions that are needed in Bayesian inference on pulsar-timing-array datasets. The resulting viewpoint and formalism lead us to two improved parameter-sampling schemes inspired by Gibbs sampling. The new schemes have vastly lower chain autocorrelation lengths than the Markov Chain Monte Carlo methods currently used in pulsar-timing data analysis, potentially speeding up Bayesian inference by orders of magnitude. The new schemes can be used for a full-noise-model analysis of the large datasets assembled by the International Pulsar Timing Array collaboration, which present a serious computational challenge to existing methods.

22 pages, 4 figures

References in corpus (47)

• Tests of general relativity from timing the double pulsar
• The international pulsar timing array project: using pulsars as a gravitational wave detector
• Gravitational radiation from cosmic (super)strings: bursts, stochastic background, and observational windows
• The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays
• The Parkes Pulsar Timing Array Project
• The North American Nanohertz Observatory for Gravitational Waves
• Gravitational Waves Probe the Coalescence Rate of Massive Black Hole Binaries
• Limits on the Stochastic Gravitational Wave Background from the North American Nanohertz Observatory for Gravitational Waves
• Upper bounds on the low-frequency stochastic gravitational wave background from pulsar timing observations: current limits and future prospects
• Gravitational wave stochastic background from cosmic (super)strings
• Placing limits on the stochastic gravitational-wave background using European Pulsar Timing Array data
• Detecting the stochastic gravitational wave background using pulsar timing
• Assessing the Role of Spin Noise in the Precision Timing of Millisecond Pulsars
• The International Pulsar Timing Array
• Optimal strategies for gravitational wave stochastic background searches in pulsar timing data
• The stochastic background: scaling laws and time to detection for pulsar timing arrays
• Measurement and correction of variations in interstellar dispersion in high-precision pulsar timing
• The Parkes Pulsar Timing Array
• Systematic investigation of the expected gravitational wave signal from supermassive black hole binaries in the pulsar timing band
• On measuring the gravitational-wave background using Pulsar Timing Arrays
• TempoNest: A Bayesian approach to pulsar timing analysis
• Gravitational wave astronomy of single sources with a pulsar timing array
• Development of a pulsar-based timescale
• Constraining the properties of the proposed supermassive black hole system in 3c66b: Limits from pulsar timing
• Pulsar timing analysis in the presence of correlated noise
• Gravitational-wave Limits from Pulsar Timing Constrain Supermassive Black Hole Evolution
• Characterising gravitational wave stochastic background anisotropy with Pulsar Timing Arrays
• Detection of gravitational waves from the QCD phase transition with pulsar timing arrays
• Understanding and analysing time-correlated stochastic signals in pulsar timing
• Measuring the parameters of massive black hole binary systems with Pulsar Timing Array observations of gravitational waves
• Dispersion Measure Variations and their Effect on Precision Pulsar Timing
• Stochastic backgrounds in alternative theories of gravity: overlap reduction functions for pulsar timing arrays
• Hyper-efficient model-independent Bayesian method for the analysis of pulsar timing data
• Searching For Anisotropic Gravitational-wave Backgrounds Using Pulsar Timing Arrays
• The Sensitivity of the Parkes Pulsar Timing Array to Individual Sources of Gravitational Waves
• Resolving multiple supermassive black hole binaries with pulsar timing arrays
• Optimal strategies for continuous gravitational wave detection in pulsar timing arrays
• Gravitational-wave memory and pulsar timing arrays
• Relic Gravitational Waves and Cosmology
• Elementary Wideband Timing of Radio Pulsars
• Model-based asymptotically optimal dispersion measure correction for pulsar timing
• The optimal schedule for pulsar timing array observations
• Pulsar Timing Sensitivities to Gravitational Waves from Relativistic Metric Theories of Gravity
• Resolving multiple supermassive black hole binaries with pulsar timing arrays II: genetic algorithm implementation
• Bayesian inference for pulsar timing models
• Accelerating pulsar timing data analysis
• Pulsar timing and the detection of black hole binary systems in globular clusters

Cited by in corpus (84)

• The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
• Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array
• The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals
• The NANOGrav 12.5-year Data Set: Search For An Isotropic Stochastic Gravitational-Wave Background
• European Pulsar Timing Array Limits On An Isotropic Stochastic Gravitational-Wave Background
• Detection methods for stochastic gravitational-wave backgrounds: a unified treatment
• The International Pulsar Timing Array: First Data Release
• The NANOGrav Nine-year Data Set: Limits on the Isotropic Stochastic Gravitational Wave Background
• Common-red-signal analysis with 24-yr high-precision timing of the European Pulsar Timing Array: Inferences in the stochastic gravitational-wave background search
• Wotan: Comprehensive time-series de-trending in Python
• The NANOGrav Nine-year Data Set: Observations, Arrival Time Measurements, and Analysis of 37 Millisecond Pulsars
• Pulsar Timing Array Constraints on Primordial Black Holes with NANOGrav 11-Year Data Set
• The gravitational-wave background null hypothesis: Characterizing noise in millisecond pulsar arrival times with the Parkes Pulsar Timing Array
• The NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget
• From Spin Noise to Systematics: Stochastic Processes in the First International Pulsar Timing Array Data Release
• The NANOGrav 12.5-year Data Set: Wideband Timing of 47 Millisecond Pulsars
• Testing Theories of Gravitation Using 21-Year Timing of Pulsar Binary J1713+0747
• Identifying and mitigating noise sources in precision pulsar timing data sets
• The second data release from the European Pulsar Timing Array II. Customised pulsar noise models for spatially correlated gravitational waves
• The MeerKAT Pulsar Timing Array: The first search for gravitational waves with the MeerKAT radio telescope
• Mining Gravitational-wave Catalogs To Understand Binary Stellar Evolution: A New Hierarchical Bayesian Framework
• From Bright Binaries To Bumpy Backgrounds: Mapping Realistic Gravitational Wave Skies With Pulsar-Timing Arrays
• Modeling the uncertainties of solar-system ephemerides for robust gravitational-wave searches with pulsar timing arrays
• The Need For Speed: Rapid Refitting Techniques for Bayesian Spectral Characterization of the Gravitational Wave Background Using PTAs
• Non-tensorial Gravitational Wave Background in NANOGrav 12.5-Year Data Set
• Searching for continuous Gravitational Waves in the second data release of the International Pulsar Timing Array
• The second data release from the European Pulsar Timing Array V. Search for continuous gravitational wave signals
• Limits on anisotropy in the nanohertz stochastic gravitational-wave background
• Constraints On The Dynamical Environments Of Supermassive Black-hole Binaries Using Pulsar-timing Arrays
• Frequency-Dependent Template Profiles for High Precision Pulsar Timing
• Detecting eccentric supermassive black hole binaries with pulsar timing arrays: Resolvable source strategies
• Low-rank approximations for large stationary covariance matrices, as used in the Bayesian and generalized-least-squares analysis of pulsar-timing data
• Noise analysis in the European Pulsar Timing Array data release 2 and its implications on the gravitational-wave background search
• Novel Method for Incorporating Model Uncertainties into Gravitational Wave Parameter Estimates
• TDI-infinity: time-delay interferometry without delays
• Bayesian Implications for the Primordial Black Holes from NANOGrav's Pulsar-Timing Data Using the Scalar-Induced Gravitational Waves
• The NANOGrav 11-Year Data Set: Evolution of Gravitational Wave Background Statistics
• The NANOGrav 15-year Gravitational-Wave Background Methods
• Accurate characterization of the stochastic gravitational-wave background with pulsar timing arrays by likelihood reweighting
• Model Dependence of Bayesian Gravitational-Wave Background Statistics for Pulsar Timing Arrays
• Quality over Quantity: Optimizing pulsar timing array analysis for stochastic and continuous gravitational wave signals
• Practical approaches to analyzing PTA data: Cosmic strings with six pulsars
• Bayesian Solar Wind Modeling with Pulsar Timing Arrays
• Taming outliers in pulsar-timing datasets with hierarchical likelihoods and Hamiltonian sampling
• Is there a spectral turnover in the spin noise of millisecond pulsars?
• Rapid and accurate parameter inference for coalescing, precessing compact binaries
• Searching for quasi-periodic oscillations in astrophysical transients using Gaussian processes
• Ephemeris Errors and the Gravitational Wave Signal: Harmonic Mode Coupling in Pulsar Timing Array Searches
• 21st Century Statistical and Computational Challenges in Astrophysics
• Pulsar Timing Arrays require hierarchical models
• Exploring the time variability of the Solar Wind using LOFAR pulsar data
• How to Detect an Astrophysical Nanohertz Gravitational-Wave Background
• Charting the Nanohertz Gravitational Wave Sky with Pulsar Timing Arrays
• Noise analysis of the Indian Pulsar Timing Array data release I
• Posterior predictive checking for gravitational-wave detection with pulsar timing arrays: I. The optimal statistic
• Harmonic analysis for pulsar timing arrays
• Exploring the Capabilities of Gibbs Sampling in Pulsar Timing Arrays
• Efficient Gravitational Wave Searches with Pulsar Timing Arrays using Hamiltonian Monte Carlo
• Use Model Averaging instead of Model Selection in Pulsar Timing
• Implementation of an efficient Bayesian search for gravitational wave bursts with memory in pulsar timing array data
• On tests of general relativity with binary radio pulsars
• Solving the PTA Data Analysis Problem with a Global Gibbs Scheme
• Ensemble noise properties of the European Pulsar Timing Array
• Bayesian cross validation for gravitational-wave searches in pulsar-timing array data
• Toward a test of Gaussianity of a gravitational wave background
• Posterior predictive checking for gravitational-wave detection with pulsar timing arrays: II. Posterior predictive distributions and pseudo Bayes factors
• The 31-year Rotation History of the Millisecond Pulsar J1939+2134 (B1937+21)
• Regularizing the Pulsar Timing Array likelihood: A path towards Fourier Space
• The Chinese Pulsar Timing Array data release I. Single pulsar noise analysis
• Impact of the observation frequency coverage on the significance of a gravitational wave background detection in PTA data
• Low-frequency pulse-jitter measurement with the uGMRT I : PSR J0437$-$4715
• The ORT and the uGMRT Pulsar Monitoring Program : Pulsar Timing Irregularities & the Gaussian Process Realization
• Rapid Construction of Joint Pulsar Timing Array Datasets: The Lite Method
• The Indian Pulsar Timing Array Data Release 2: II. Customised Single-Pulsar Noise Analysis and Noise Budget
• An updated constraint for the Gravitational Wave Background from the Gamma-ray Pulsar Timing Array
• Rapid inference for individual binaries and a stochastic background with pulsar timing array data
• Improving DM estimates using low-frequency scattering-broadening estimates
• On the calculation of p-values for quadratic statistics in Pulsar Timing Arrays
• Revisiting wideband pulsar timing measurements
• Timing Gamma-ray Pulsars using Gibbs Sampling
• New Metrics for Identifying Variables and Transients in Large Astronomical Surveys
• The NANOGrav 15 yr Data Set: Customized Chromatic Noise Models
• A Parallelized Bayesian Approach To Accelerated Gravitational-Wave Background Characterization
• Searching Stochastic Gravitational Wave Background Landscape Across Frequency Bands