I am a PhD student in Phonetics and I have been doing statistical analyses of speech data for a long time now. I am quite familiar with the hands-on side of data analysis with R and Python, such as organizing the dataset, plotting distributions, checking for tests' assumptions, run linear regressions, and so forth. However, I am not completely happy with my knowledge because, even though I have an intuitive understanding of inferential statistics and I am very careful to make sure that I am not doing anything stupid with my data, I don't understand the mathematical theory behind statistical inference. Since I have a workable knowledge of basic math (for example, I know the basics of linear algebra, single-variable and multivariable calculus), I think it's time to try to learn once for all the foundations of statistics.

So I looked for introductory books on mathematical statistics that had undergrads as the main audience, to ensure that I would be able to follow the math.

In particular, I started reading All of Statistics: A Concise Course in Statistical Inference by Larry Wasserman. Even though I am enjoying it and being able to follow the math, I am still struggling to make the connections between what I am learning (e.g., random variables, CDF, PDF, etc.) and my experience with data analysis. I mean, I am still not able to visualize the big picture and understand how to transfer this formal knowledge to my data analysis practices.

I would like recommendations of books or resources that are similar to All of Statistics but that present the mathematical theory of statistical inference in the context of actual scientific data analyses.