# Fast Parameter Inference on Pulsar Timing Arrays with Normalizing Flows

arXiv: https://arxiv.org/abs/2310.12209 · HTML: https://mlsanity.com/paper/2310.12209/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 47 references that are in the map.
- First posted on arXiv 18 Oct 2023.

## Builds on (most cited first, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition](https://mlsanity.com/paper/1402.1128/) (2014)
- [Deep Learning for Real-time Gravitational Wave Detection and Parameter Estimation: Results with Advanced LIGO Data](https://mlsanity.com/paper/1711.03121/) (2017)
- [Image-based deep learning for classification of noise transients in gravitational wave detectors](https://mlsanity.com/paper/1803.09933/) (2018)

## Built on by (most cited first, 2 of 2)

- [Preconditioned Neural Posterior Estimation for Likelihood-free Inference](https://mlsanity.com/paper/2404.13557/) (2024)
- [Preconditioned Robust Neural Posterior Estimation for Misspecified Simulators](https://mlsanity.com/paper/2602.18004/) (2026)

## Abstract (arXiv)

Pulsar timing arrays (PTAs) perform Bayesian posterior inference with expensive MCMC methods. Given a dataset of ~10-100 pulsars and O(10^3) timing residuals each, producing a posterior distribution for the stochastic gravitational wave background (SGWB) can take days to a week. The computational bottleneck arises because the likelihood evaluation required for MCMC is extremely costly when considering the dimensionality of the search space. Fortunately, generating simulated data is fast, so modern simulation-based inference techniques can be brought to bear on the problem. In this paper, we demonstrate how conditional normalizing flows trained on simulated data can be used for extremely fast and accurate estimation of the SGWB posteriors, reducing the sampling time from weeks to a matter of seconds.