Reading: “Statistique pour mathématiciens” (V. Panaretos)

I’m going to be using the summer break to get some reading done. I’ll do one or more post on every book I read so that I can share a little bit of what I learn.

Today, I’ll discuss “Statistique pour mathématiciens, un premier cours rigoureux” which is a second year Bachelor course aimed at mathematicians which is used in EPFL. I’m reading it because I’m teaching the same course but for engineers next fall, and I’m hoping to find some good ideas about how to explain statistics.

As I write the post, I have read about half of the book (which is fairly short: 240 pages, including a 100 page-long appendix with proofs and exercise corrections). However, it is extremely dense and full of content. It reminds me of “All of statistics” by Wasserman in that this book could be a very good first dive into statistics for someone who feels comfortable with probability theory but who has no knowledge of statistics. Of course, given that it is much shorter that “All of statistics”, it doesn’t have the same depth or breadth, but this book has all the essential points of statistics.

One section which I particularly liked was the introduction. It seems to me that all of the major difficulties of statistics are conceptual: once you understand what you are trying to accomplish, and the way you should frame your questions, the math part of statistics is (should be?) straightforward compared to other classes. However, these conceptual difficulties are either glossed over or very poorly presented. Panaretos does a great job of explaining exactly what statistics is and how it proceeds.

One particularly great example of this is when he describes how one should choose a model to describe a dataset: through a handful of clear and (at least for engineers) familiar examples, he gives great examples of how scientific, philosophical, or exploratory approaches can be used and combined to formulate an appropriate model.

 

I look forward to finishing reading this very nice book !

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