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!
 A: 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).
A: I would recommend following two books:


*

*Statistical methods for bioinformatics 

*The elements of statistical learning
