First of all, I see a lot of possibility that there is a misunderstanding here, both on your part, and on my part in reading this.
The reason for this is that I have found that a lot of people don't quite have a clear idea of what is "theoretical physics", confusing it with being confined to just "String, GUT, TOE, elementary particles". In reality, "theoretical physics" is actually a vague area, because ANY area of physics, including "applied" ones, have theoretical components. This means that "statistical physics" can also already be a subset of this "theoretical physics", which makes the question rather puzzling. It is like asking if the aorta valve has any role to play in the human body. So this is something I am not sure that everyone who brings up the phrase "theoretical physics" is aware of.
Secondly, upon re-read your post, I am wondering if you actually mean "statistical analysis", i.e. the methodology, rather than the subject area.
Without a clear idea of the actual question and the actual intent of the question, I don't know if any clear answer can be given.
Zz.