In time, big data comes to all disciplines. It doesn't come to all of them at the same time, but it will come to all of them in the same period.
When big data comes to your discipline, you will want quantitative methods, because you will want computational practices. Generally speaking, quantitative methods are statistical in nature.
Somehow, quantitative methods seem less controversial when applied to "non-living nature:" we don't see a problem with the idea that mathematical principles should govern the orbit of stars or the formation of crystals or the erosion of soil. But biology and the humanities have, historically, shared a certain disdain for quantitative methods, as being an oversimplification of the wonderfully idiosyncratic and messy problems presented by "living nature." We are interested in an organic whole, in the organism.
"Biology asks six kinds of questions. How is it built? How does it work? What goes wrong? How is it fixed? How did it begin? What is it for? These are questions, respectively, about structures, mechanisms, pathologies, repairs, origins, and functions or purposes." -- Joel Cohen, "Mathematics Is s Next Microscope, Only Better; Biology Is Next Physics, Only Better"
What would the humanities version of those questions be? I think they'd be substantially the same, but there'd be more of a who in the how and the what. Intention, or at least consciousness, is what might--or might not--make a difference between the objects of attention in biology and in the (secular) humanities. Secular humanists have a tortured relationship with intention, of course, and we've come up with lots of systemic explanations for the individual actor, but fundamentally we do believe that cultural artifacts are somehow intended, and that this makes them different from other artifacts of nature.
So, in each case, a discipline grows up around the observation and description of living organisms in an organic systems, and in both cases at some point enough of the data about those organisms and systems is available in digital form to allow statistical analysis, at first as a method of description or modeling, and then as a method of prediction, a tool for hypothesis-building, and an empirical check on certain kinds of truth-claims.
Talk about the history and theory of the cross-over in terms of "ensemble" -- the idea of doing things together. Shared horizons, you know. But consider the implications of "ensemble" in