Addressing prior dependence in hierarchical Bayesian modeling for PTA data analysis II: Noise and SGWB inference through parameter decorrelation
Pulsar Timing Arrays (PTA) provide a powerful framework to measure low-frequency gravitational waves, but accuracy and robustness of the results are challenged by complex noise processes that must be accurately modeled. Standard PTA analyses assign fixed uniform noise priors to each pulsar, an approach that can introduce systematic biases when combining the array. To overcome this limitation, we adopt a hierarchical Bayesian modeling strategy in which noise priors are parametrized by higher-level hyperparameters. To mitigate the sensitivity of the inferred parameters to the choice of noise hyperprior, we introduce a reparametrization of the hierarchical model based on the orthogonal projection of hyperparameters onto the physical parameter subspace. The transformation is implemented through Normalizing Flows (NFs), which provide an invertible, tractable representation and preserve shrinkage and inter-pulsar information pooling in the reparametrized model. We also employ i-nessai, a flow-guided nested sampler, to efficiently explore the resulting higher-dimensional parameter space. We apply our method to a minimal 3-pulsar case study, performing a simultaneous inference of noise and stochastic gravitational wave background (SGWB) parameters. Despite the limited dataset, the results consistently show that the reparametrized hierarchical treatment constrains the noise parameters more tightly and partially alleviates the red-noise-SGWB degeneracy, while the orthogonal reparametrization further enhances parameter independence without affecting the correlations intrinsic to the power-law modeling of the physical processes involved.