So something that no one usually admits is that there are three types of reasoning about stuff (frequentist, bayesian, and nonparametric), and each of them has

So something that no one usually admits is that there are three types of reasoning about stuff (frequentist, bayesian, and nonparametric), and each of them has their pros and cons and circumstances to use them. So with frequentist statistics, it is really easy to reason about what should be the correct estimator (it is almost always the obvious one). For example, with functional time series (where each data point is a function and not a real value), then it is straight forward to find an MLE - it is just the average function. But defining a prior on the space of twice differentiable functions isn't as easy.