This question was inspired by two recent interactions I had, one here in CV, the other over at economics.se.
There, I had posted an answer to the well-known "Envelope Paradox" (mind you, not as the "correct answer" but as the answer flowing from specific assumptions about the structure of the situation). After a time a user posted a critical comment, and I engaged in conversation trying to understand his point. It was obvious that he was thinking the Bayesian way, and kept talking about priors -and then it dawned on me, and I said to my self:"Wait a minute, who said anything about any prior? In the way I have formulated the problem, there are no priors here, they just don't enter the picture, and don't need to".
Recently, I saw this answer here in CV, about the meaning of Statistical Independence. I commented to the author that his sentence
"... if events are statistically independent then (by definition) we cannot learn about one from observing the other."
was blatantly wrong. In a comment exchange, he kept returning to the issue of (his words)
"Wouldn't "learning" mean changing our beliefs about a thing based on observation of another? If so, doesn't independence (definitionally) preclude this?
Once again, it was obvious that he was thinking the Bayesian way, and that he considered self-evident that we start by some beliefs (i.e. a prior), and then the issue is how we can change/update them. But how the first-first belief is created?
Since science must conform to reality, I note that situations exist were the human beings involved have no priors (I, for one thing, walk into situations without any prior all the time -and please don't argue that I do have priors but I just don't realize it, let's spare ourselves bogus psychoanalysis here).
Since I happened to have heard the term "uninformative priors", I break my question in two parts, and I am pretty certain that users here that are savvy in Bayesian theory, know exactly what I am about to ask:
Q1: Is the absence of a prior equivalent (in the strict theoretical sense) to having an uninformative prior?
If the answer to Q1 is "Yes" (with some elaboration please), then it means that the Bayesian approach is applicable universally and from the beginning, since in any instance the human being involved declares "I have no priors" we can supplement in its place a prior that is uninformative for the case at hand.
But if the answer to Q1 is "No", then Q2 comes along:
Q2 : If the answer to Q1 is "No", does this mean that, in cases where there are no priors, the Bayesian approach is not applicable from the beginning, and we have to first form a prior by some non-Bayesian way, so that we can subsequently apply the Bayesian approach?