Rapid parameter estimation for pulsar-timing-array datasets with variational inference and normalizing flows

TL;DR

This paper presents a fast, neural network-based variational inference method for pulsar-timing-array data analysis, significantly reducing computation time compared to traditional MCMC techniques, enabling new astrophysical insights.

Contribution

The authors introduce a neural network-based variational inference approach for pulsar-timing data, trained for single datasets, offering a highly parallelizable and faster alternative to MCMC methods.

Findings

Analyzed NANOGrav 15-yr dataset in tens of minutes.

Achieved faster parameter estimation than traditional methods.

Potential for broader application in gravitational-wave data analysis.

Abstract

In the gravitational-wave analysis of pulsar-timing-array datasets, parameter estimation is usually performed using Markov Chain Monte Carlo methods to explore posterior probability densities. We introduce an alternative procedure that relies instead on stochastic gradient-descent Bayesian variational inference, whereby we obtain the weights of a neural-network approximation of the posterior by minimizing the Kullback-Leibler divergence of the approximation from the exact posterior. This technique is distinct from simulation-based inference with normalizing flows, since we train the network for a single dataset, rather than the population of all possible datasets, and we require the computation of the data likelihood and its gradient. Unlike Markov Chain methods, our technique can transparently exploit highly parallel computing platforms. This makes it extremely fast on modern graphical processing units, where it can analyze the NANOGrav 15-yr dataset in few tens of minutes, depending on the probabilistic model, as opposed to hours or days with the analysis codes used until now. We expect that this speed will unlock new kinds of astrophysical and cosmological studies of pulsar-timing-array datasets. Furthermore, variational inference would be viable in other contexts of gravitational-wave data analysis as long as differentiable and parallelizable likelihoods are available.