I have two normal distributions representing the posterior distribution of two alternate physical models.
In this physical problem I would like to know which model is more likely to produce a value greater than $n$. I can calculate the probability of a value greater than $n$ for both distributions using the normal cumulative distribution function.
Assuming both models had the same prior probability, can I calculate the evidence for each model using the Bayes factor calculated with the probabilities from the CDF?
It is a messy problem because I am trying to compare two models generated using different sets of observations (so I know the likelihood relative to that data), but what I would like to know the likelihood of each model producing values greater than $n$ which is a threshold value.