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I'm going to apply to graduate programs in both Statistics and Data Science. To me, Statistics, Data Science, and Machine Learning essentially refers to the same subject, but some universities are offering different programs. Still, it's rare for a program in Statistics to not mention DS/ML at all, and vice versa.

My undergraduate major is in Statistics, but my research experiences is mostly concerned with Machine Learning. When writing my Statement of Purpose, I'm struggle to justify why I'm applying to STAT programs with a background in DS/ML. Yeah, they are closely related, but wouldn't it be weird to say "Through my research experience in DS/ML, I developed an interest in STAT, so I'm applying to your STAT program"? The reason I'm applying to a STAT program instead of that in DS when both are offered is that the former is generally more academic, theoretical, and in-depth. (AFAIK there are no Ph.D. programs in DS, but it's hard to find a STAT Ph.D. whose research interest is not related to DS/ML.) I cannot say for now whether I'm going to work in academic or in industry, but I believe a sound theoretical background would be helpful in either case.

I don't think claiming STAT, DS, and ML are the same in the SOP would be a good idea either, as the Committee probably won't agree with me. How do I address the issue of terminologies, then?

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wouldn't it be weird to say "Through my research experience in DS/ML, I developed an interest in STAT, so I'm applying to your STAT program"?

I don't think so, especially if you modify it a bit:

"My experience as a STAT major, combined with my research experiences in DS/ML, have inspired me to further study STAT."

I think you can, and should, blend the two together. As you noted, they are related, and the committees know this. Use that to your advantage.

If you are applying to a school with both and you feel like you must justify your choice of STAT over another program, then I think you've already got your justification: you are drawn to the theoretical and rigorous nature of the program. I think your major is more than enough to prevent you from seeming like an outsider.

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