# A good book with equal stress on theory and math

I have had enough courses on statistics during my school years and at the university. I have a fair understanding of the concepts, such as, CI, p-values, interpreting statistical significance, multiple testing, correlation, simple linear regression (with least squares) (general linear models), and all tests of hypothesis. I had been introduced to it much of the earlier days mostly mathematically. And lately, with the help of the book Intuitive Biostatistics I have grasped and unprecedented understanding towards the actual conceptual theory, I believe.

Now, what I find I lack is understanding of fitting models (estimating parameters to model) and the like. In particular, concepts such as maximum likelihood estimation, generalized linear models, bayesian approaches to inferential statistics always seem foreign to me. There aren't enough examples or tutorials or conceptually sound ones, as one would find on simple probabilistic models or on other (basic) topics on the internet.

I am a bioinformatician and I work on RNA-Seq data which deals with raw read counts towards finding, lets say, gene expression (or differential gene expression). From my background, even if I am not familiar with statistical models, I am able to grasp the reason for a poisson distribution assumption and negative binomials and so on.. But some papers deal with generalized linear models and estimate a MLE etc.. which I believe I have the necessary background to understand.

I guess what I am asking for is an approach some experts among you deem useful and (a) book(s) which helps me grasp these concepts in a more intuitive way (not just rigorous math, but theory backed with math). As I am mostly going to apply them, I would be satisfied (at the moment) with understanding what is what and later, I can go back to rigorous mathematical proofs... Does anyone have any recommendations? I don't mind buying more than 1 book if the topics I asked for are indeed scattered to be covered in a book.

Thank you very much!

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Could you recommend me some good sources to learn about RNA-Seq data and statistical challenges in this field? –  Biostat Oct 18 '11 at 13:12
biostat, sure, the website seqanswers.com is a very good resource for NGS. You could start with the different technologies and how they work from here: goo.gl/NLuvJ These are some papers that explain some statistical problems with NGS data. In short, they are technical and biological variance estimation (with regard to gene expression). 1) One of the first papers assessing technical variation: ncbi.nlm.nih.gov/pubmed/18550803 2) DESeq: a tool for gene expression detection: ncbi.nlm.nih.gov/pubmed?term=DESeq%20simon%20anders –  Arun Oct 18 '11 at 15:39
Converted to CW because it looks like a bunch of good suggestions will be offered and there is no apparent objective standard to decide a "best" among them. I hope this will make it easier for readers to vote up lots of the replies, too :-). –  whuber Oct 18 '11 at 16:15
whuber, sure! makes sense. Can I make a community wiki post? or it requires moderator privileges? –  Arun Oct 18 '11 at 17:15
@Arun: Thank you very much! –  Biostat Oct 18 '11 at 18:37

You will find everything non-Bayesian that you asked about it Frank Harrell's Regression Modeling Strategies. I would leave Bayesian recommendations to more knowledgeable folks (although I do have Gelman, Carlin, Stern and Rubin, as well as Gilks, Richardson and Speigelhalter, on my bookshelf). There should be a few Bayesian biostat books on the market.

Update: McCullach and Nelder (1989) is a classic book on GLMs, of course. It was groundbreaking for its time, but I find it rather boring, frankly. Besides, it does not cover the later additions like residual diagnostics, zero-inflated models, or multilevel/hierarchical extensions. Hardin and Hilbe (2007) cover some of this newer stuff in good details with practical examples in Stata (where GLMs and extensions are very well implemented; Hardin used to work at Stata Corp. writing many of these commands, as well as contributing to the sandwich estimator).

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Hi StasK, thank you very much! I find the one on regression modeling would cater to my requirements. How much do they cover GLMs? I also see that your references on Bayesian inference are the standard ones I always find recommended. In your opinion, how easy/difficult are they to follow (as in if the level is too advanced)? Also, have you had a look at the book Generalized linear models? One of the authors is J.A. Nelder. Also, I'd like to also buy this book on statistical models. Do you have any thoughts on this one? Thanks! –  Arun Oct 18 '11 at 17:24
I have not seen this Freedman's book. It is a pretty interesting one, although it seems to be rather light in terms of rigor, and I am not sure I am happy with that. (A book that is very light on math that talks about regression without matrix algebra, but VERY deep on scientific rigor, is Mostly Harmless Econometrics by Angrist and Pischke, and if you work with causal models, this book is a must.) I don't really know your math/stat background, so it will be hard for me to judge if these books would be difficult. Some Bayesian books might be; they tend to assume you already know MLE and GLM. –  StasK Oct 19 '11 at 15:17
I've updated my response to include McCullach and Nelder reference. –  StasK Oct 19 '11 at 15:25
I am a electronics engr. turned bioinformatician. I have had courses on statistics (for communication theory), probability and random processes, am comfortable with calculus (although a bit rusty) and also linear algebra. Of course these are mostly undergraduate level... My objective is to be conceptually sound (more of geometric interpretations, understanding of the methods and most importantly the purpose) etc... Of course, I don't mind the math, if it comes along with these recipes. Thanks again for your recommendations! –  Arun Oct 20 '11 at 0:29