Before the interview, HR sends you an email with a book list and the HR says the interview will be based on knowledge of these books. Depending on your background, these books are either quite elementary or quite advanced. They range from machine learning, theoretical statistics, convex analysis, computer science theory, to stochastic calculus (so in all, about 10 books or so).
For a guy who'd spent substantial amount of time (weeks!) reviewing said book list, I was somewhat disappointed by the actual interviews. (Note: Other than some pieces here and there, I already had good exposure to the topics on the book list from previous studies. So it was more or less a review for me). For one, the interview questions themselves don't really seem to relate to the books at all. And for those questions that do seem to relate to the book list, they are so subtle that unless you'd already spent decent amount of course time to study these things, you'd never be able to answer their question with just a few weeks.
Beyond the book list, however, is the way they assess candidates. A good number of interviewers simply want you to walk through a recent project that you'd done. I think this is a fair (and probably only) method of assessment of candidates with a masters and/or PhD. However, some interviewers like to ask about your project --- then afterwards throw out brainteasers. It's insulting to say the least. To take an analogy of what I'm saying: it's as if I'd just told the interviewer I did a whole thesis on stochastic partial differential equations on Banach spaces, and then you end the chat with me by asking brainteaser questions on cards / dice combinatorics. I very well could fumble this brainteaser question (i.e. it was not even hinted at in their book list nor is it related to the research project I told you), but failing that brainteaser equates to a No in their eyes. But I guess they take whether answering brainteasers as a benchmark for intelligence rather than showcasing an original piece of research (contrast this to their job posting description).
All in all --- I'm simply confused at what they want. Do you want people who have knowledge of the book list? Do you want people who exhibit some unique perspectives via their recent research projects? Or do you want people who ace brainteasers? It's quite clear those three objectives are quite mutually exclusive.