Bayesian methods can’t compete with Conformal Prediction (CP not CF). There are multiple reasons for it, CP does not require prior, is non parametric and works with any distribution and any underlying model whether statistical, machine learning or deep learning. More importantly Bayesian methods have no theoretical guarantees of validity (lack of bias) unless the data has been synthetically generated using known priors. The outcome of Bayesian methods is posterior in the wrong place with the wrong shape. You can read more here https://arxiv.org/abs/2107.00363 and follow me on LInkedIn to learn more also join Awesome Conformal Prediction slack (link in the repo).