Bayesian inference of $W$-boson mass

We use a Bayesian regression technique (similar to a recent analysis by Rinaldi et al) to obtain a central estimate for the $W$-boson mass using four different combinations of datasets compiled by the PDG including the 2022 CDF result. We use three different priors on the unknown intrinsic scatter and also a non-parametric hierarchical Dirichlet Process Gaussian Mixture model to obtain a world average for $W$-boson mass. We also evaluate the statistical significance of the discrepancy with respect to the Standard model for each of the datasets. We find that for all the combination of datasets and the aformentioned prior choices, the discrepancy with respect to the Standard Model value for the $W$-mass is less than 3$\sigma$. We also checked that if we use a narrow prior on the intrinsic scatter, we get a discrepancy of about 3.8$\sigma$ compared to the Standard model value.