Solving the PTA Data Analysis Problem with a Global Gibbs Scheme

Abstract

The announcement in the summer of 2023 about the discovery of evidence for a gravitational wave background (GWB) using pulsar timing arrays (PTAs) has ignited both the PTA and the larger scientific community's interest in the experiment and the scientific implications of its findings. As a result, numerous scientific works have been published analyzing and further developing various aspects of the experiment, from performing tests of gravity to improving the efficiency of the current data analysis techniques. In this regard, we contribute to the recent advancements in the field of PTAs by presenting the most general, agnostic, per-frequency Bayesian search for a low-frequency (red) noise process in these data. Our new method involves the use of a conjugate Jeffrey's-like multivariate prior which allows one to model all unique parameters of the global PTA-level red noise covariance matrix as a separate model parameter for which a marginalized posterior-probability distribution can be found using Gibbs sampling. Even though perfecting the implementation of the Gibbs sampling and mitigating the numerical stability challenges require further development, we show the power of this new method by analyzing realistic and theoretical PTA simulated data sets. We show how our technique is consistent with the more restricted standard techniques in recovering both the auto and the cross-spectrum of pulsars' low-frequency (red) noise. Furthermore, we highlight ways to approximately characterize a GWB (both its auto- and cross-spectrum) using Fourier coefficient estimates from single-pulsar and so-called CURN (common uncorrelated red noise) analyses via analytic draws from a specific Inverse-Wishart distribution.

Published at https://link.aps.org/doi/10.1103/PhysRevD.111.063067

References in corpus (27)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• 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 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 15-year Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational Wave Background
• The International Pulsar Timing Array second data release: Search for an isotropic Gravitational Wave Background
• The NANOGrav Nine-year Data Set: Limits on the Isotropic Stochastic Gravitational Wave Background
• The gravitational-wave background null hypothesis: Characterizing noise in millisecond pulsar arrival times with the Parkes Pulsar Timing Array
• Hyper-efficient model-independent Bayesian method for the analysis of pulsar timing data
• New advances in the Gaussian-process approach to pulsar-timing data analysis
• Astrophysics Milestones For Pulsar Timing Array Gravitational Wave Detection
• The NANOGrav 12.5-year Data Set: Wideband Timing of 47 Millisecond Pulsars
• The Need For Speed: Rapid Refitting Techniques for Bayesian Spectral Characterization of the Gravitational Wave Background Using PTAs
• Noise-marginalized optimal statistic: A robust hybrid frequentist-Bayesian statistic for the stochastic gravitational-wave background in pulsar timing arrays
• Low-rank approximations for large stationary covariance matrices, as used in the Bayesian and generalized-least-squares analysis of pulsar-timing data
• Common-spectrum process versus cross-correlation for gravitational-wave searches using pulsar timing arrays
• The MeerKAT Pulsar Timing Array: The $4.5$-year data release and the noise and stochastic signals of the millisecond pulsar population
• Subluminal stochastic gravitational waves in pulsar-timing arrays and astrometry
• Model Dependence of Bayesian Gravitational-Wave Background Statistics for Pulsar Timing Arrays
• Pulsar Timing Arrays require hierarchical models
• Spatial and Spectral Characterization of the Gravitational-wave Background with the PTA Optimal Statistic
• Exploring the Capabilities of Gibbs Sampling in Pulsar Timing Arrays
• Efficient Gravitational Wave Searches with Pulsar Timing Arrays using Hamiltonian Monte Carlo
• Controlling Outlier Contamination In Multimessenger Time-domain Searches For Supermasssive Binary Black Holes

Cited by in corpus (4)

• Rapid Construction of Joint Pulsar Timing Array Datasets: The Lite Method
• Rapid inference for individual binaries and a stochastic background with pulsar timing array data
• The NANOGrav 15 yr Data Set: Customized Chromatic Noise Models
• Full analytic expressions of overlap reduction functions for anisotropies of the stochastic gravitational-wave background with pulsar timing arrays