I am looking for a textbook (or, more likely, a set of textbooks) in English for self-education in probability and mathematical statistics.
I’m a middle-aged person working as data scientist, primarily in market research. I’ve been doing data mining, machine learning, sometimes business modeling, etc. for many years. Now when I have achieved some degree of professional success, I feel that my lack of theoretical education is holding me back from further development.
For example, I can do some relatively sophisticated factor or cluster analysis with Python (mostly using
scikit-learn), and I have some basic idea of underlying math behind applied methods, but I’ve never truly understood this math in depth.
Ideally, I’d like to be able to trace the derivation of each statistical test or other application from the very outset—not only in order to comprehend their workings, but to modify them for my situations and to develop plausible derivative applications as well. For example, I’ve written a little module for nominal-ordinal association testing based on some academic papers, but I was only able to convert the described methods into code without real insight into why they work at all. I’d better like to be able to explain every detail of these methods to myself and to any interested person from, say, a high-school level.
I tried to search for the textbooks myself, mostly by investigating search results by Best Textbooks on [Something], but I got completely lost. It is as I should learn some set theory, some combinatorics, some measure theory, some topology, lots of calculus, lots of linear algebra, and probably something else—and this is just to get on with the probability theory. Even if I somehow choose the “best” book on each topic (based on my goals) and get through it, I will be a mess due to huge amount of information and conceptual incompatibility between books (different approaches, scientific communities, explanation methods, notation etc.).
So, I need your advice on what to start with. I’m not afraid of serious and niche literature as long as I can see it can help in my situation; I’m far more afraid of books like σ-Fields Comic Book for Dummies.