You're thinking like a Bayesian - I avoided using those terms, but that's essentially the latter approach. The prior knowledge is built into the model with our

You're thinking like a Bayesian - I avoided using those terms, but that's essentially the latter approach. The prior knowledge is built into the model with our choice of the functions and the weights that we assign those functions. (It should be noted that the Bayesian approach doesn't guarantee a defined answer - we can easily have a divide-by-zero/undefined value in that school of thought as well. However, the frequentist approach always leads to an undefined outcome in this question, because it follows from the definition of probability itself, whereas in the Bayesian approach, it follows from insufficient information in the model specification.)