What can I read to give me a meta-view of statistics as a field

Question

What can I read that will give me a meta-view of the diverse field of statistics and data science? With few exceptions much of what I get my hands of goes straight into formulae and methodologies. Preferably something sufficiently high level as to bring in diverse areas such as econometrics, psychometrics, machine learning, etc.

To be more concrete, preferably something that:

• Summarises and discusses the various branches of statistics/data science; what problems are encountered in each branch.
• Talks about differences between the branches and their histories.
• Contrasts methodological approach.

Answer 1

I guess I would like to read or at least browse in that too, but only a polymath or a committee could write it, and the polymath isn't evident and committee books often don't work well. Also, many of the general books on statistics that tend to pop up from (e.g.) searches on Amazon just leave out most of the interesting technical details and/or are written by people not close to any cutting edge.

But I would recommend browsing in the Encyclopedia of Statistical Sciences if a library near you holds a copy:

http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471150444.html

and also that you look through what appears in Statistical Science, which has a good track record of readable review and discussion papers.

I would venture an assertion that most specialists in econometrics, psychometrics, machine learning, etc. would have little confidence that people outside their own field really understand what is currently central and most interesting in that field. (So, what else is new?)

Answer 2

There's Barnett (2009), Comparative Statistical Inference, which does a good job of contrasting different methodologies, with only as much maths as necessary. Nothing on Machine Learning though—some of the references here may be useful (& indeed the answers).

A survey of different areas of application (psychometrics, econometrics, &c.) would be interesting, & I hope someone can suggest one.

Answer 3

I remember that reading The lady tasting tea by Salsburg gave me a lot to think about. Even tough the historical perspective of the book may not be exactly what you're looking for, it makes for a fun and quick read.

If you can get a copy of Stochastic Musings, it might prove an interesting read. It's probably a bit too technical for your needs, but I'd recommend the more "relaxed" pieces by Cox and Efron among others to give you an idea of the breadth of the discipline.