Modeling Foreground Spatial Variations in 21 cm Gaussian Process Component Separation

Gaussian processes (GPs) have been extensively utilized as nonparametric models for component separation in 21 cm data analyses. This exploits the distinct spectral behavior of the cosmological and foreground signals, which are modeled through the GP covariance kernel. Previous approaches have employed a global GP kernel along all lines of sight (LoS). In this work, we study Bayesian approaches that allow for spatial variations in foreground kernel parameters, testing them against simulated HI intensity mapping observations. We consider a no-pooling (NP) model, which treats each LoS independently by fitting for separate covariance kernels, and a hierarchical Gaussian Process (HGP) model that allows for variation in kernel parameters between different LoS, regularized through a global hyperprior. We find that accounting for spatial variations in the GP kernel parameters results in a significant improvement in cosmological signal recovery, achieving up to a 30% reduction in the standard deviation of the residual distribution and improved model predictive performance. Allowing for spatial variations in GP kernel parameters also improves the recovery of the HI power spectra and wavelet scattering transform coefficients. Whilst the NP model achieves superior recovery as measured by the residual distribution, it demands extensive computational resources, faces formidable convergence challenges, and is prone to overfitting. Conversely, the HGP model strikes a balance between the accuracy and robustness of the signal recovery. Further improvements to the HGP model will require more physically motivated modeling of foreground spatial variations.