A classic example of overfitting
Which model do you believe?
The complicated model fits the
data better.
But it is not economical and it
makes silly predictions.
But what if we start with a reasonable
prior over all fifth-order polynomials
and use the full posterior distribution.
Now we get vague and sensible
predictions.
There is no reason why the amount of
data should influence our prior beliefs
about the complexity of the model.