Frequentist statistical mechanics

Yes. So you got your ensemble. Jaynes says every member of the ensemble is equally probable due to ignorance. Another interpretation is that of those using the "ergodic hypothesis" where one postulates that a specific system will in due time (on the order of poincaré recurrence time, i.e. VERY FRIGGIN LONG) pass every point on phase phase arbitrarily close. Since every member of the ensemble corresponds with one phase space point, in the frequentist definition of probability every member of the ensemble becomes equally probable. Jaynes criticized this by saying that the recurrence time is absurdishly long and that when you make a measurement, it's on the order of seconds, not age-of-the-universe. Of course there are also many critiques on the bayesian interpretation. As far as I know, it hasn't been conclusively settled (?)