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Statistical Inference v.s. Machine learning?

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Hi all, I am a rising senior in stats major. I am going to apply for PhD programs in stats in 20 Fall. This fall, I have the option to take statistical inference (Casella, G. and Berger) or machine learning (known to be one of the most interesting and useful CS courses at my institution). They are offered at the same time. I heard statistical inference is helpful for PhD application while machine learning is also a super popular topic in stats. I am interested in both theoretical and computing area of stats so that it is hard to make up my mind. Can anyone give some advice? Thank you very much :)

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Casella and Berger is the core of your first year of courses in a MS/PhD program and will be theory-based.   I'd recommend you take that because it will 100% help you in a PhD program. 

Machine learning is likely to be more of a survey course with some applications and coding. It might help you become familiar with some common methods and get some experience coding, but it's unlikely to provide that base of knowledge that will help you in a PhD program.  On the other hand, it is always helpful to know the ML buzzwords if you want an industry data science job.  I highly doubt an undergraduate ML course will go into much depth of the theory.

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