I studied datamining and textmining in library school! :)

The field you're looking for is called digital history or digital humanities, though it's an "emerging field" which means no one really knows what it means. But on a basic level, I'd encourage you not to think of datamining and statistical analysis as something that needs a particular historic field to be useful, instead, these are all techniques that can and have been applied to many different fields of history.

Maybe you learned this one in school already, but there is a classic example in textmining which is analyzing the disputed authorship of the Federalist Papers. I'm also guessing you know about the idea of literature-based discovery from the late Don Swanson's pioneering methods on medical literature? I haven't seen this applied to history literature yet, but I think there is a lot of potential in this method to find new historical links.

There are a lot of historical data sets out there that are simply waiting for someone to put them in a machine-readable format. I'm personally at my archives sitting on 40 years of tax records in microfilm that we're trying to get digitized and put in machine readable format, we only need about half a million to do it... :)

Census data, most basically, has already been used for a lot of studies. Take a look at James Loewen's work on Sundown Towns. He worked first off census data and went back to fill in the gaps using newspaper data and oral history, an approach that would have been doable before that data was digitized, surely, but probably never done, because it would have been too laborious. Digital makes a lot of things possible, or at least condenses them from a lifetimes work to a few years work.

GIS data is verrrry popular with historians right now. I went to this presentation and it was like, maps all around, map everything.

So there's a lot of potential in digital techniques and tools if you'd like to try your hand at history. :)

Aside from what /u/caffarelli said about the digital humanities/history field (and its vagaries), you might want to look into the (re?)emerging field of computational history, which calls itself that to clarify that it is about the sorts of things you are interested in (data mining, statistical approaches to the past, applying quantitative methods from the sciences, etc.).

All of this is emerging and messy at the moment so finding easy paths forward is not obvious. If I were in your place, I would try to find people doing things of the character that I was interested in, and getting in touch with them and asking about what kinds of opportunities might be available, what kinds of work you would need to do to seem useful (and not dilettantish — historians are not going to be a priori impressed that a science student is interested in helping them become more "scientific," and may resent it if you don't phrase it right).

I put the (re?) in front of "emerging" because I just want to hint that these kinds of attempts, though going through some resurgence in interest, are not especially new. There have been attempts at doing this sort of thing for many decades. The results have generally not impressed or made huge impacts on the field of history, and applying quantitative methods to the past never been as big a factor in the formal study of history as they are in overlapping fields like economics, political science, etc. So a lot of historians (and I count myself among them) are a little suspicious that this is really going to further the discipline in interesting ways (but I try to be open-minded). That being said, there are a lot of recent calls for Big Data approaches to the past (e.g. The History Manifesto), and there are groups of historians, philosophers, and scientists at various places developing new tools to try and apply statistical tools to the past. (Because I am classed under the big, messy umbrella of 'digital history' I find myself at a lot of events with the people who do this in the history of science, even though we have little uniting our methods or interests except for the fact that we all use computers in some non-obvious way, which becomes less of a unifying theme over time.)

If I were advising someone from the sciences who was interested in history (which is not an uncommon thing in my discipline, the history of science), what I would do is recommend you read up a bit on historiography — on the different approaches that have been made to the study of the past. Because this is the area that typically distinguishes the history "buff" from someone who can make real contributions to the field. The "buff" is interested in the facts and the stories; the real contributor is someone who understands how we should think about approaching the past. And if you are interested in doing non-trivial things with computers, you have to think very carefully about how we ought to think about the past, because you are going to have to think about what kinds of data you are going to be using (what kind of information you are going to have access to, how you are going to structure it, what you can learn from it, what you can't, etc.). Without that you end up just recapitulating the same kinds of dull studies (word frequency, simple citation counting, etc.) that make up a lot of the underwhelming aspects of digital history. The Computational History and Philosophy of Science group at ASU is doing some very interesting and non-obvious things with these kinds of tools, as an aside.