Rapid Parameter Estimation for Pulsar-Timing-Array Datasets with Variational Inference and Normalizing Flows.

Area of Science:

• Astrophysics
• Cosmology
• Data Analysis

Background:

• Parameter estimation in gravitational-wave analysis of pulsar-timing-array (PTA) datasets typically uses Markov chain Monte Carlo (MCMC) methods.
• MCMC methods explore posterior probability densities but can be computationally intensive and time-consuming.

Purpose of the Study:

• To introduce a novel, computationally efficient alternative to MCMC for parameter estimation in PTA data analysis.
• To leverage neural networks and Bayesian variational inference for faster and more scalable data analysis.

Main Methods:

• Developed a stochastic gradient-descent Bayesian variational inference procedure.
• Utilized a neural network to approximate the posterior probability density.
• Minimized the Kullback-Leibler divergence between the approximate and exact posteriors.
• Trained the network on a single dataset, differing from simulation-based inference.

Main Results:

• The new technique significantly accelerates the analysis of PTA datasets, particularly on parallel computing platforms like GPUs.
• Analysis of the NANOGrav 15-yr dataset was completed in tens of minutes, a substantial improvement over hours or days with MCMC.
• The method requires computation of the data likelihood and its gradient.

Conclusions:

• This fast variational inference technique offers a viable alternative for gravitational-wave data analysis.
• The speedup enables new astrophysical and cosmological explorations with computationally expensive statistical models.
• The approach is applicable to other gravitational-wave data analysis contexts with differentiable and parallelizable likelihoods.