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.

翻译：脉冲星计时阵为测量低频引力波提供了强大框架，但结果的准确性和稳健性受到必须精确建模的复杂噪声过程的挑战。标准脉冲星计时阵分析为每颗脉冲星分配固定的均匀噪声先验，这种方法在组合阵列时可能引入系统性偏差。为克服此局限性，我们采用分层贝叶斯建模策略，其中噪声先验由更高层级的超参数参数化。为减轻推断参数对噪声超先验选择的敏感性，我们引入基于超参数向物理参数子空间正交投影的分层模型重新参数化。该变换通过归一化流实现，其可逆且易处理的表示形式在重参数化模型中保留了收缩效应和脉冲星间信息聚合。我们还采用流引导型嵌套采样器i-nessai高效探索由此产生的高维参数空间。我们将该方法应用于最小三脉冲星案例研究，同步推断噪声和随机引力波背景参数。尽管数据集有限，结果一致表明：重参数化分层处理能更严格约束噪声参数并部分缓解红噪声-随机引力波背景简并问题，而正交重参数化则在不影响物理过程幂律建模固有相关性的前提下进一步增强参数独立性。