If the model is y = a + b * x + e, then we can precisely state probability distributions of a and b given x and y for reasonably general assumptions about error

If the model is y = a + b * x + e, then we can precisely state probability distributions of a and b given x and y for reasonably general assumptions about error e. If the model is y = f(x) + e, where for example f is a neural net, there is not much we can say about the “quality” of parameters of f. That is, we can’t attach confidence interval. We will have to resort to expensive simulations and for most practical applications this is not workable (size of dataset). What you say is useful in a different context. Local linearization is a very powerful idea.