
Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years -- at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information, even breaking Germany's Enigma code during World War II, and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security. Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time. - Publisher.
She tells a terrific story with a fascinating large cast of characters including Laplace,Bayes,Fisher,Pearson,Jeffries,Savage,Turing and many others. Engagingly told, highly recommended. Could the takeaway "Do you want to solve a practical problem or do you want scientific rigor?"
and here's a video for the most common question I get about bayes vs frequentist
https://www.youtube.com/watch?v=foSPfzYs4yY
For recommendations here's my suggestions split by persona
* I want a PHD in statistics or to write novel research - Go read BDA3 cover to cover. Gelman etal are amazing, and amazingly brilliant. The book is dense though, even after years of experience I need to now read chapters 2 or 3 times and write out proofs
* I want have a smooth on ramp into Bayesian stats with lots of code and beautiful writing. I also like video lectures and undergraduate college courses - Statistical Rethinking. As noted below Richard does a wonderful job explaining these concepts with metaphors like golems, interspersing it with this experience as an anthropologist, and using his teaching experience to write well structured introduction into Bayesian stats. This book does assume you understand basic statistics and probability theory.
* I want a great comparison of Bayesian vs Frequentist stats- This book covers both topics well, compares them fairly, and has all the proofs to back things up https://www.routledge.com/Understanding-Advanced-Statistical...
* I'm a programmer type person that likes hands on "build from scratch" using code - Allen Downey's think bayes builds up bayes theorem from Numpy arrays. He's also a brilliant instructors
* I want to read about the history and people and politics - Bernoulli's fallacy, The Theory That Would Not Die:, and Probably Overthinking it are all "non mathy" great armchair readings https://cup.columbia.edu/book/bernoullis-fallacy/97802311999... https://www.amazon.com/Theory-That-Would-Not-Die/dp/03001882... https://www.allendowney.com/blog/
* Im an applied practitioner that is focusing more on my specific problem and I need to use the latest PPLs and code to get it done - This is my book. I had to make estimations in SpaceX supply chain with some quick deadlines and I didn't have time to take an undergrad course. I also needed my code to be robust, testable, and scalable. I didn't find that other books provided this so that's why I wrote this with CRC and Osvaldo. Osvaldo and I are heavy contributors to PyMC, ArviZ, Preliz and other libraries so naturally we take a code first approach. https://bayesiancomputationbook.com/welcome.html
* (Shameless self promotion) Im a professional, I need to learn fast, and my company will pay for training - For this specific niche me and other Bayesian colleagues created an online course designed specifically for professionals. Yes it's expensive so let me plainly state no one at any point needs to spend any money to learn Bayesian stats. That being said hundreds of people have purchased this course and the feedback we've gotten on this course has been quite positive. So I want to underscore before Hacker news rips me apart. No one is being forced to buy this, if you want this style course here it is, if you don't there's many many ways to learn Bayesian stats. https://www.intuitivebayes.com/
You can sign up for the Gaussian Process course for free if you'd like https://www.intuitivebayes.com/gaussian-processes
As you can tell I'm very fascinated by generative modeling. I find it fun to think about. I also frankly find it lucrative. It's helped me job hop across some pretty cool companies and get through the Google interview. The combination of strong programming skillset with applied generative mathematics is only heating up so I feel lucky to have chanced upon it, and also thankful that many others before me put great code and reading material out there so I could learn myself.
Also not exactly what was asked, but so good: James Gleick’s ”Information”. It is about the history of information theory or how to statistically argue about information. Really starts from the beginning, eg. how some tribes used drums to talk to each other over kilometers away.
[1]https://www.amazon.com/Theory-That-Would-Not-Die/dp/03001882...
Edit: How to by Randall Munroe for the math-comedy realm.