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I have been doing Machine Learning for a while and have worked with things like probability models, MCMC, variational inference, kernel methods, time series etc.

I am looking a for a book to complement my statistics knowledge. The book should not ideally revisit things that are mostly covered in ML books or elementary probability theory books but should explore things like survey sampling, a/b testing, experiment design, quantitative marketing, counterfactuals, visualization and summarization of findings etc. It would be much better if the book is more intuitive than rigorous, and shorter/more concise the better for me.

Overall, I am looking for a book that can give me a glimpse of how a statistician approaches data science problems.

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I think Statistics for Experimenters by Box, Hunter, and Hunter, while over 30 years old, gives a lot of insight into how Statisticians approach problems. Particularly the "Science and Statistics" and "Empirical Modeling" chapters.

A very concise statement of how more "classical" statisticians approach problems is given by the great D. R. Cox in his book with Christl Donnell, "Principles of Applied Statistics".

Two other statistics books I like a lot are "Statistical Rethinking" by Richard Mcelreath and "Statistics Done Wrong" by Alex Reinhart. The former is a textbook while the latter is a very readable slim volume. I'm not sure if these last two are what you're looking for, but I think worth checking out regardless.

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  • $\begingroup$ I think the OP wants books that specifically deal with machine learning. I don't see how your references include that topic. $\endgroup$
    – Michael R. Chernick
    Jun 23, 2017 at 15:22
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    $\begingroup$ Maybe I misread but it sounded to me like OP wanted statistics books that don't retread standard ML ground. I tried to pick some books I enjoyed that are more in the how a statistician might approach a problem vein and not just textbooks on the topics he specifically mentioned. $\endgroup$
    – FledglingStat
    Jun 23, 2017 at 16:33
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    $\begingroup$ Stat The title of the question is misleading. I think you are right based on the last sentence n the question. That was my mistake. By the way I very much like Statistics for Experimenter also. $\endgroup$
    – Michael R. Chernick
    Jun 23, 2017 at 19:39
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    $\begingroup$ Thanks for the references. @MichaelChernick Yeah, I am not looking for a book that covers standard ML stuff, if you have a better recommendation for the title I am happy to change it. $\endgroup$
    – jkt
    Jun 24, 2017 at 18:53

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