Answer by Justin Rising:
These are the books that I've found helpful. This is by no means a complete list–and in particular, I'm not trying to cover anything beyond the core topics–but it is a solid start. As always, my recommendations tell you as much about my biases and interests as they do anything else.
Applied Statistics and Statistical Computing
- ) is hands down the best introductory book for statistical thinking. There's almost no math in here, but reading this and doing the exercises will force you to engage with the material.
- is a perfectly good introduction to basic applied statistics.
- is a more advanced course on applied statistics with an emphasis on computational methods. All of the methods it uses are available in R, so you can use it without S-Plus.
- is an introduction to programming in R. You won't find a lot of statistics in here, but it's still material that you need to know.
- is another good book on programming in R.
- is a nice introduction to linear regression for someone with a strong background in linear algebra.
- is the only reasonable choice for starting out with applied Bayesian methods.
- is a fantastic introduction to very important class of regression models. This one is accessible to a wide audience.
- is a classical text on machine learning methods. I'm not going to try to give a comprehensive list of books on ML, but I wouldn't feel right completely leaving it out, and this is still the standard by which other books are judged.
Mathematical Statistics and Statistical Theory
- I learned my basic theory from. It's a good book, but there's a lot that it doesn't cover.
- is the standard book on mathematical statistics. It's still missing some stuff, but this is definitely essential.
- is a more advanced book on inference that covers statistical decision theory. If you want to really understand statistical methods, you have to understand the basics of that framework.
- is an introduction to the theory of linear models as opposed to their applications. Even if you want to do applied statistics you need to understand this stuff on a basic level.
- can be viewed as a second course in linear models that deals with some very useful special cases. This is pretty dry, but it's thorough and fairly clear.
- is a reference book on classical multivariate methods. Basically, if you can assume multivariate normality, this book has something on your problem.
- is the standard introduction to classical asymptotics.
- is a more modern and encyclopedic book on asymptotics.
- is a more mathematical introduction to Bayesian statistics. I could put this one in the applied statistics section, but it's not wrong to put it here either.
Probability and Stochastic Processes
- I learned undergraduate probability from), which is a fine introductory book that covers all the standard topics.
- I also like, which is another good introduction that has some topics that are a little less standard. If you want to prepare for the actuarial exam on probability, this is a very good book to read.
- I usedfor my undergraduate stochastic process course. It's a very standard introductory book.
- For a slightly more advanced stochastic processes textbook, I recommend. For most work, this will have pretty much everything you need.
- But if it doesn't, you can probably find what you're looking for in eitheror .
- is a nice book on probability and stochastic processes that covers some unusual topics. It's meant to be accessible to non-mathematicians, although you still have to be mathematically literate.
- If you want (or need) to get into actual probability theory,is a very good place to start. It's very clearly written with a good emphasis on understanding what's going on.
- is a more rigorous book that's still clear with a lot of examples.
- Of course, you will have to engage withThis is the standard reference for probability theory, and almost everything that a non-probabilist could need is in here. It's also the standard textbook for a graduate-level probability theory course, but you will find it helpful to supplement it with something else.
- is a gentle and intuitive introduction to stochastic calculus. It's more aimed at someone who wants to use stochastic calculus than the hardcore theoreticians.
- If you do want to be a hardcore theoretician,is the place to start.
- Last but certainly not least, I'm going to throw in a recommendation for. You can't really understand a subject until you've made a few wrong conjectures and learned why they're off, and this book probably talks about some things you'll believe by the time you get here.