In a quote very reminiscent of statistics, Arnold Sommerfeld said:
Thermodynamics is a funny subject. The first time you go through it, you don’t understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don’t understand it, but by that time you are so used to it, it doesn’t bother you any more. 
For my second pass at statistics, I focused on developing intuition and techniques for real-world applications. Here are a collection of resources that were useful for for me.
- Risk Analysis of the Space Shuttle: Pre-Challenger Prediction of Failure
Looks back on the ill-fated Challenger disaster and attempts to use better statistical analysis to measure accident risk.
- Stein’s Paradox in Statistics
An extremely readable introduction to the Stein Paradox. We learn that when we have more than 3 gaussians, the best estimator of the their means is not the sample mean!
- What is the Chance of an Earthquake?
A non-mathematical paper which discusses what probabilities mean using a fascinating case study.
Other Lists of Papers
As I sift through the papers here, I’ll move the ones I like up into my list.
- Xi’an’s List
Have not gone through everything here yet, but they seem very promising.
- Andrew Gelman’s List and Another
A few gems, but many are presently out of reach for me. Better luck on the third pass perhaps.
- Larry Wasserman’s
- How can we improve hypothesis testing to take into account seasonality effects present in the responses of the control and treatment groups of an experiment?
- During data analysis, one often has to decide on the most informative ways to segment the dataset. What is a good measure of high-signal segmentation? Can we apply information theory concepts like mutual information? What about machine learning classification? What if we need confidence intervals around these metrics?
- Why is it when we use the sample variance to estimate the population variance, we need to renormalize by n/n-1? (See Bassel’s Correction) This and this are halfway good answers.
- What is it about statistics that makes it (seem?) so much harder to learn than, say, Physics?
Much thanks to Olivia Angiuli for piggybacking me on her adventure through statistics grad school, and Anirudh Sankar for intriguing discussions.
 Arnold Sommerfeld, as quoted in Salvatore Califano’s Pathways to Modern Chemical Physics (2012) and by many other science authors (Wikipedia)