Making sense out of statistics theory and applications I have recently graduated with my masters degree on medical and biological modeling, accompanied with engineering mathematics as a background. Even though my education program included a significant amount of courses on mathematical statistics (see below for a list), which I managed with pretty high grades,  I frequently end up completely lost staring down on both theory and applications of statistics. I have to say, compared to "pure" mathematics, statistics really makes little sense to me. Especially the notations and language used by most statisticians (including my past lecturers) is annoyingly convoluted and almost none of the resources I have seen so far (including wikipedia) had simple examples that one could easily relate to, and associate to the theory given...
This being the background; I also realize the bitter reality that I cannot have career as a researcher/engineer without a firm grip on statistics, especially within the field of bioinformatics.
I was hoping that I could get some tips from more experienced statisticians/mathematicians. How can I overcome this problem I have mentioned above? DO you know of any good resources; such as books, e-books, open courses (via iTunes or OpenCourseware for ex) etc.. 
EDIT: As I have mentioned I am quite biased (negatively) towards a majority of the literature under general title of statistics, and since I can't buy a number of large (and expensive) coursebooks per branch of statistics, what I would need in terms of a book is something similar to what Tipler & Mosca
is for Physics, but instead for statistics. 
For those who don't know about Tipler; it's a large textbook that covers a wide majority of the subjects that one might encounter during higher studies, and presents them each from basic introduction to slightly deeper in detail. Basically a perfect reference book, bought it during my first year in uni, still use it every once in a while.

The courses I have taken on statistics:


*

*a large introduction course, 

*stationary stochastic processes,

*Markov processes,

*Monte Carlo methods

*Survival analysis

 A: I can completely understand your situation. Even though I am PhD student, I find it hard sometimes to related theory and application. If you are willing to immerse yourself in understanding theory, it is definitely rewarding when you think about real world problems. But the process may be frustrating.
One of the many references that I like is Gelman and Hill's Data Analysis Using Hierarchical/Multilevel Models. They avoid the theory where they can express the underlying concept using simulations. It will definitely benefit you as you have experience in MCMC etc. As you say, you are working in bioinformatics, probably Harrell's Regression Modeling Strategies is a great reference too.
I will make this a community wiki and let others add to it.
A: Are you familiar with Bayesian Data Analysis (by Gelman, Carlin, Stern, and Rubin)? Maybe that's what you need a dose of.
A: All statistics problems essentialy boils to following 4 steps (which I borrowed from @whuber answer on another question):


*

*Estimate the parameter.

*Assess the quality of that estimate.

*Explore the data.

*Evaluate the fit.
You can exchange word parameter with word model. 
Statistics books usually present the first two points for various situations. The problem that each real world application requires different approach, hence different model, so a large part of the books end up cataloguing these different models. This has undesired effect that it is easy to lose yourself in the details and miss the big picture. 
The big picture book which I heartily recommend is Asymptotic statistics. It gives a rigorous treatment of the topic and is mathematically "pure". Though its title mentions asymptotic statistics, the big untold secret is that majority of classical statistics methods are in essence based on asymptotic results. 
A: I think the most important thing here is to develop an intuition about statistics and some general statistical concepts.  Perhaps the best way to do this is to have some domain that you can "own."  This can provide a positive feedback loop where understanding about the domain helps you to understand more about the underlying statistics, which helps you to understand more about the domain, etc.
For me that domain was baseball stats.  I understood that a batter that goes 3 for 4 in a game is not a "true" .750 hitter.  This helps to understand the more general point that the sample data is not the same as the underlying distribution.  I also know he is probably closer to an average player than to a .750 hitter, so this helps to understand concepts like regression to the mean.  From there I can get to full-blown Bayesian inference where my prior probability distribution had a mean of that of the mean baseball player, and I now have 4 new samples with which to update my posterior distribution.
I don't know what that domain is for you, but I would guess it would be more helpful than a mere textbook.  Examples help to understand the theory, which helps to understand the examples.  A textbook with examples is nice, but unless you can make those examples "yours" then I wonder if you will get enough from them.
A: As an alternative to Regression Modeling Strategies, and for a more practical approach, Applied Linear Statistical Models is very good from my point of view.
A: Everyone learns differently, but I think it's safe to say that examples, examples, examples, help a lot in statistics.    My suggestion would be to learn R (just the basics are enough to help a lot) and then you can try any and every example until your eyes bleed.  You can sort it, fit it, plot it, you name it.   And, since R is geared toward statistics, as you learn R, you'll be learning statistics.   Those books that you listed can then be attacked from a "show me" point of view.
Since R is free, and a lot of source material is free, all you need to invest is your time.
http://www.mayin.org/ajayshah/KB/R/index.html
http://math.illinoisstate.edu/dhkim/rstuff/rtutor.html
http://www.cyclismo.org/tutorial/R/
http://www.stat.pitt.edu/stoffer/tsa2/R_time_series_quick_fix.htm
http://www.statmethods.net/about/books.html
There are many good books on R that you can buy, here's one that I've used:
http://www.amazon.com/Introductory-Statistics-R-Peter-Dalgaard/dp/0387954759
Edit============
I forgot to add a couple of links.   If you're using Windows, a good editor to feed R is Tinn-R (someone else can add links for editors on a Mac, or Linux).
http://www.sciviews.org/Tinn-R/
http://cran.r-project.org/web/packages/TinnR/
A: I personally loved this which had a really good mix of theory and application (with lots of examples). It was a good match with casella and berger for a more theory oriented approach. And for a broad brush overview this.
