A non-subjective account of statistical mechanics close to the treatment with large deviation theory (which is just a more abstract version of it) is given in Part II of my online book
Classical and Quantum Mechanics via Lie algebras, http://arxiv.org/abs/0810.1019
At the end (in Sections 10.6 and 10.7), one also finds a short discussion of the subjective, information theoretic treatment and its deficiencies.
A survey that treats statistical mechanics directly in terms of large deviations is given in (reference  of the book, referenced on p.208)
R.S. Ellis. An overview of the theory of large deviations and applications to statistical
mechanics. Scand. Actuarial J, 1:97–142, 1995.
A more recent survey is:
H. Touchette, The large deviation approach to statistical mechanics, Phys. Rep. 478 (2009), 1-69.