I love all the recommendations here but please say a word or two about why you recommend said books. Sell them to me, don't make me do the work. Dumb lists of titles are so uninteresting.
ok, i will try.
2 books I absolutely love and have read cover to cover several times, solved most of the 1000+ problems.
1. Inference - Rohatgi
2. Inference - Stapleton
Why I recommend them ? The real answer is super long. But the short version is - there are thinkers & there are doers. Basically, the mathematical statistics world has these theory-building Bourbaki type guys who write a LOT, say a LOT, but never get to the fucking point (imho). The opposite view is "math is bunch of tricks. its like chess - more middlegames & endgames you know, higher chance of winning. No real point in learning who originally came up with this particular middle game variation, or why does this opening work etc etc. Just learn the trick & play the game." So that's the eastern (Indian/Chinese) school of thought, which is what I subscribe to.
The 2 inference books listed above are essentially grab-bags of tricks. Do this - it works - now try it on these problems - ok next trick...on & on. So I solved the 1000+ problems & now I know lots of these methods that just work.
eg. recently i was asked - some vc's are evaluating a startup. their valuations are $1 million, $4 M,$10M, $20M, $50M. what's your evaluation & why ?
so i'm thinking - hey isn't this just rohatgi taxicar ? so i quickly said- sum is 85, times 1/5 is 17. Whereas largest observed is 50, times 6/5 is 60, so half is 30. since 50 was max observed, another estimator is half that, ie. 25. if you want doctor's estimate, get rid of 1 and 50, then sum is 34 so times 1/3 is 11.3
so then we have 4 estimators, - the sample mean is 17 million, its the method of moments estimator, clearly unbiased but high mean square error because variance is high. the maximum likelihood estimator is 25 mil, and has smallest variance, but the mse will not be the lowest since it is not unbiased so bias square will add. the 30 mil estimate is also unbiased, but has low variance so it has the lowest mse of the lot. the doctor estimator 11 million is unbiased but high variance and mse is in between. now if you want the absolute lowest mse, i can cook up a 5th estimator which has nonzero bias but mse will be the minimum....
at this point the interviewer interrupts me - you've never seen this problem because we came up with it in our last meeting at our firm. Yet you gave me 4 very good estimators under 2 minutes & want to cook up a 5th one that's even better. And you don't even have a phd. meanwhile i just spoke to an actual phd and asked him this same question, he went on and on for 20 minutes without giving me a single concrete estimator!
so that's the thing. rohatgi, stapleton, these are about real world, down & dirty, how to do stuff. how to solve actual problems.
whereas the gelman bda, the shao, the schervish, the lehman, the bickel & doksum - these were my prescribed textbooks. imho they are absolute garbage, worse than dirt. after the exam i threw them away. such bullcrap. they go on & on without getting anywhere & have practically zero good worked examples.
so that's my 2 cents. i still have the rohatgi & stapleton on my desk. sometimes i tear up when i look at them. they have taught me so, so much!
In other words: have the tricks, when crashed against the real world over and over like you describe, oozed into something akin to a larger theoretical sense of things? Or do they remain isolated tricks that you apply when they seem to match?
(I wish I could frame this question better, but I don't know this field, sadly.)
Someone once wrote this. If someone gives you Excalibur, you don't fucking ask where it came from, who made it, etc. Just go use it and have fun.
(a mostly-hypothetical question)
But I think they also have their intuitions built from experience in the sense of Tao's post-rigorous stage: https://terrytao.wordpress.com/career-advice/theres-more-to-...
I find your comment amusing considering:
1. You just wrote 5 paragraphs of anecdotes.
2. Bourbaki Elements of Mathematics is the driest book you can think about. It’s mostly formal definitions and extremely rigorous demonstrations.
Your snide costs you a lot of credibility at least as far as I’m concerned.
My personal 2ct: first understand how to solve "real" problems, then move on to the abstract theory. I cannot understand the theoretical mathematics behind a concept if I don't have at least one non-trivial example in my head which I understand completely.
What's your advice in the self-learning prerequisites knowledge/materials before being able to digest those books?
My last math course was calculus I and II back in first year uni 15 years ago as well as stats I and II on my second year (which I completely bamboozled and forgot the material as soon as I barely pass the class).
The most information-dense form of book recommendation possible is probably a “dumb” list consisting largely of books one knows and appreciates, with one or two new titles in addition. I’ll probably learn more about where a person recommending a book I haven’t read is coming from based on a list of their favorites than I will from the text of a hastily constructed review.
In any case, I wouldn’t dismiss someone out of hand for providing a “dumb” list.
In particular the handful of volumes that pertain to my established laboratory & field work, as well as possible aspirational efforts.
It can really pay to keep up to date.
Also, the text/content of all the standards are the work of volunteer technical people, who come to complete consensus before the well-paid journalist professionals at the nonprofit publisher send it to press.
ASTM may contain some of the most statistically documented laboratory procedures for repeatabiliy & reproducibility compared to what you normally find.
A lot of the books people have commented on have been influential in the past and do stand on their own today.
Well even though outdated ASTM standards may have limited value, one real offsetting benefit is the past experience of using them in previous years when they were current and some standards were less fully developed.
So if you think about it, the current year's publication is a snapshot, the majority of your collection from previous years is huge by comparison, and ends up proportionally more helpful on the whole, even though somewhat outdated or even obsolete.
And these books are hefty, they weigh kilos per year and cost the big bucks.
Not really worth it either unless you're really ready to dip deeply into the unique type of bureaucracy associated with these type of efforts.
But it gets much worse, you think ASTM books are boring, how about the Federal Register?
There's another ongoing publication where the bureaucracy is so thick, someone can specialize so highly at navigating it that they can more effectively win bids without any technical qualifications compared to actual practicioners, most of whom don't stand a chance on merit alone. Not for me, but if you're aiming for Uncle Sam's pocketbook you need to up your game here.
I guess there are a lot of other books which might inspire people to take some action of their own, or even build a business around. Not always ones that are intended to be inspirational either.
Some people think Buckminster Fuller was inspirational, one of my handful of books when I had a shelf is Earth, Inc.
Title sounds almost like the name of a business or something:
https://books.google.ca/books?id=l5DODQAAQBAJ&pg=PP5&source=...
Only about a half inch thick, fits on any shelf with ease, not for people that dislike big words. You have been warned.
Then for electronics it's Radiotron. Specifically RDH4:
https://archive.org/details/bitsavers_rcaRadiotr1954_9495850...
Not so thin, 1523 pages mainly for people that do really like equations.
If you can build projects like they have here, I guarantee you will be able to do things your peers will not.
Both published decades ago, so it's up to the reader to fill in the blanks about how we got to where we are now.
I like to have moments to myself without feeling like I am being sold something. I feel like I am constantly being sold things on the internet; let me do the discovery myself. Let me decide for myself whether or not it is interesting to me.