I have taken a handful of statistics/ data science-oriented courses. And to this day, I feel like I grasp the underlying concept but I do not comprehend the in-depth understanding. I am asking this because it's been more of a formulaic relationship, and since it is so applicable and important, I was wondering if anybody had any readings or mental breakthroughs to what Bayes Theorem is!
I would highly recommend this video by the youtube channel 3blue1brown, as it is the best intuitive and visual explanation for Bayes Theorem:
The creator Grant makes many videos on a variety of different topics in Mathematics from calculus, to linear algebra, to even neural networks, and he has a fantastic ability to explain concepts in a way that helps you understand it, rather than just learning it to be able to use it.
As a side note, he also has a follow up video on Bayes Theorem that will perhaps help relate it to your previous understanding of it:
Besides 3blue1brown (which was a major help to me in this and other concepts I wasn't really 'getting'), one thing that made it click for me was manually going through some examples and doing the math by hand (old school, pen and paper) in an iterative fashion so that I can actually see the posteriors update in front of my eyes.
Sounds like middle school stuff, but to me it made a difference versus only reading materials and, like you said, feeling like I only grasp the underlying concept.
I had said mental breakthrough when I read Data Analysis: A Bayesian Tutorial by Sivia and Skilling. It is a fantastic book that first introduces us to the Bayesian philosophy, then the theorem and then, by way of example, shows many well-known statistical methods by deriving them from Bayes Theorem.
The book is incredible to read. The authors brief without oversimplifying, also entertaining and highly informative.
I heartily recommend it to anyone who wonders what (Bayesian) probability theory is all about.