Papers like Briggs et al. 2002 say that logical constraints on inputs such as probability parameters exclude the the Normal distribution from consideration due to its unboundedness. In this example, values below 0 and above 1. They briefly describe the Bayesian derivation from the proportion data (binomial) to the beta, for use as the sampling distribution for probabilities in the probabilistic sensitivity analysis via Monte Carlo simulation. The beta can take on a normal-like shape, but it can also have very non-normal shapes.
Can this Bayesian derivation be reconciled with the frequentist central limit theorem that says with a sufficiently large sample size the sampling distribution of the sampling mean will be approximately normal? For resource use (ie. number of visits to the doctor) Briggs et al 2002 use a Gamma distribution, as shaped in Table 4, which is certainly not Normal. Normality is what would be expected for sufficiently large samples in the frequentist interpretation.
In a Monte Carlo simulation, if a Normal distribution was used to draw realized values for probabilities, there would be some iterations where values <0 or >1 are observed. However, for symmetric distributions this should cancel out asymptotically. The distribution is still centered around the mean which is within its logical bounds, and Monte Carlo considers aggregate results not results of a single iteration. So I'm wondering why we care about the logical constraints of parameters such as probabilities, costs, etc. within the context of a Monte Carlo simulation?