Statistics as practiced today (1930s until now?) consists almost entirely of making inferences about unobserved probability distributions. That includes nonparametric statistics, and frequentist versus Bayesian has nothing to do with it.
There are some probability models that are not really statistical models, but there are few or no statistical models that are not also probability models.
Least-squares regression is a probability model. Even if you don't particularly care about the error distribution, you are still estimating a conditional expectation and setting a conditional independence assumption on the residuals. If that's not a probability model, then I don't know what it is!
There are some probability models that are not really statistical models, but there are few or no statistical models that are not also probability models.
Least-squares regression is a probability model. Even if you don't particularly care about the error distribution, you are still estimating a conditional expectation and setting a conditional independence assumption on the residuals. If that's not a probability model, then I don't know what it is!