In the Bayesian viewpoint of prompt ensembling, directly computing the predictive distribution integral for an output $\mathbf{y}$ is computationally infeasible due to the potentially infinite space of possible prompts $\mathbf{x}$. To address this, methods like Monte Carlo sampling are used to approximate the integral. This involves using a manageable, finite set of sample prompts, weighted by their likelihoods given the problem, defined by the prior distribution of prompts $\Pr(\mathbf{x}|p)$.