I'm trying to understand the differences between (1) Bayesian vs frequentist; and (2) subjectivist vs objectivist.
So far my understanding (correct me if I'm wrong) is that:
(1) Bayesian vs frequentist.
- Frequentist: A probability $p$ represents a long-run frequency.
- Bayesian: A probability $p$ simply reflects our tentative state of knowledge. Given new information, we may update $p$.
(2) Subjectivist vs objectivist.
- Subjectivist: A probability is simply one's personal, subjective degree of belief about some particular matter. So two rational, intelligent people with the same information and knowledge can disagree about a probability $p$.
- Objectivist: It is impossible for two perfectly-rational people with the same information and knowledge to disagree about a probability $p$.
My understanding is that Bayesians are typically subjectivist and frequentists are typically objectivist.
However, it is possible for Bayesians to be objectivist.
My question is this: Is it possible for frequentists to be subjectivist? And how would such a subjectivist-frequentist interpret probability?