Addressing prior dependence in hierarchical Bayesian modeling for PTA data analysis I: Methodology and implementation

TL;DR

This paper introduces a novel reparameterization method using Normalizing Flows to improve hierarchical Bayesian inference in PTA data analysis, enhancing robustness and computational efficiency.

Contribution

It presents a new NF-based reparameterization strategy combined with flow-guided sampling to address prior dependence and high-dimensional challenges in PTA Bayesian modeling.

Findings

Enhanced statistical robustness in PTA inference.

Improved computational efficiency with NF reparameterization.

Effective exploration of complex posteriors using flow-guided sampling.

Abstract

Complex inference tasks, such as those encountered in Pulsar Timing Array (PTA) data analysis, rely on Bayesian frameworks. The high-dimensional parameter space and the strong interdependencies among astrophysical, pulsar noise, and nuisance parameters introduce significant challenges for efficient learning and robust inference. These challenges are emblematic of broader issues in decision science, where model over-parameterization and prior sensitivity can compromise both computational tractability and the reliability of the results. We address these issues in the framework of hierarchical Bayesian modeling by introducing a reparameterization strategy. Our approach employs Normalizing Flows (NFs) to decorrelate the parameters governing hierarchical priors from those of astrophysical interest. The use of NF-based mappings provides both the flexibility to realize the reparametrization and the tractability to preserve proper probability densities. We further adopt i-nessai, a flow-guided nested sampler, to accelerate exploration of complex posteriors. This unified use of NFs improves statistical robustness and computational efficiency, providing a principled methodology for addressing hierarchical Bayesian inference in PTA analysis.