COnformal Bayes classification

[pasq-cat]

i have some doubts on how to correctly create a conformalized bayes classifier with laplaceredux.
Laplaceredux approximate the posterior predictive distribution with a multivariate gaussian. In a second step, the predictive posterior for each input x is approximated as a Gaussian distribution. However, i do not know how, from this point, compute the conformalized bayes sets. I tried to follow section 2.4 of https://arxiv.org/pdf/2107.07511 but i did not fully understand this last step.
Can you @aangelopoulos give me a hand?

[pat-alt]

Let's double-check in Murphy p. 360