Revisiting 2D and 3D Dainotti Correlations for GRBs Using Bayesian Neural Networks

Gamma-ray bursts (GRBs) are promising cosmological probes, but their use as standard candles is limited by the circularity problem, necessitating model-independent calibration of GRB luminosity correlations. We revisit the two-dimensional (2D) and three-dimensional (3D) Dainotti correlations using Bayesian Neural Networks (BNNs) trained on the updated Observational Hubble Data (OHD) and Pantheon+ Type Ia Supernova sample. The reconstructed luminosity distances are used to calibrate the Platinum and Narendra et al. GRB samples. We constrain the parameters of the 2D Dainotti relation and the 3D fundamental plane, and examine the impact of calibration datasets and GRB sample selection. Calibration achieved using Pantheon+ yields tighter constraints than OHD, while the 3D correlation exhibits lower intrinsic scatter than the 2D relation. Our results demonstrate that BNNs provide a robust framework for model independent calibration of GRB luminosity correlations with reliable uncertainty propagation. Further, the underlying distance probe is a key factor in model-independent calibration, determining both the size of the GRB samples and the precision of the resulting constraints.