Efficient Bayesian inference and model selection for continuous gravitational waves in pulsar timing array data

TL;DR

This paper introduces a fast, efficient Bayesian inference method for analyzing gravitational wave signals in pulsar timing data, significantly reducing computation time and enabling large-scale model testing and simulations.

Contribution

The authors develop a novel Bayesian analysis approach that precalculates matrix operations, semi-analytically marginalizes over phase, and numerically marginalizes over pulsar distances, greatly improving efficiency.

Findings

Analyzes NANOGrav 15yr dataset in minutes instead of days or weeks.

Enables rapid testing of different gravitational wave models and false alarm assessments.

Facilitates large-scale simulations and model comparisons with minimal computational overhead.

Abstract

Finding and characterizing gravitational waves from individual supermassive black hole binaries is a central goal of pulsar timing array experiments, which will require analysis methods that can be efficient on our rapidly growing datasets. Here we present a novel approach built on three key elements: i) precalculating and interpolating expensive matrix operations; ii) semi-analytically marginalizing over the gravitational-wave phase at the pulsars; iii) numerically marginalizing over the pulsar distance uncertainties. With these improvements the recent NANOGrav 15yr dataset can be analyzed in minutes after an $\mathcal{O}(1\ \mathrm{hour})$ setup phase, instead of an analysis taking days-weeks with previous methods. The same setup can be used to efficiently analyze the dataset under any sinusoidal deterministic model. In particular, this will aid testing the binary hypothesis by allowing for efficient analysis of competing models (e.g. incoherent, monopolar, or dipolar sine wave model) and scrambled datasets for false alarm studies. The same setup can be updated in minutes for new realizations of the data, which enables large simulation studies.