There are 5 strong contender for best Bayesian Statistics book

TLDR

Statistical Rethinking, henceforth SR^[1]
- Up to speed fast, no integrals, very intuitive approach.
Doing Bayesian Data Analysis, henceforth The Dog Book^[2]
- This is the easiest book. If your goal is only to create simple models and you aren't interested in understanding the details, then this is the book for you.
A Student’s Guide to Bayesian Statistics, henceforth Student's Guide^[3]
- This book has the opposite focus of the Dog book. Here the author slowly goes through the philosophy of Bayes with an intuitive mathematical approach.
Regression and Other Stories, henceforth ROS^[4]
- Good you want a slower and thorough approach where you also learn the Frequentest perspective.
Bayesian Data Analysis, henceforth BDA^[5]
- The most advanced text, very math heavy, best as a second book after reading one or two of the others, unless you are already a statistician.

Irregardless of which one you pick, watching the YouTube lectures for either SR or Student's Guide is very helpful

Short review of each Book

The Dog Book: Is the easiest book is thus if you do not strive for understanding but simply want to quickly get to a skill level where you need to develop a not to fancy model then this is a great book, It is also a good reference book as each chapter is based on a specific link and function and regression variable type, thus, if you want to do an Bayesian ANOVA you simply look for chapters named something like "categorical predictor with metric outcome".

Student's Guide: This book has the opposite focus as the Dog book. Here the author slowly goes trough the philosophy of bayes with a mathematical intuitive approach. It looks like a very good reference book. A Bayesian professor has recommended it as one of the best introductions to STAN. Chapter 8 is also very good. It starts with a graph of the relationship between all likelihoods and then goes trough EACH and EVERY ONE with an intuitive example and some nice plots. I would recommend everyone to read the chapter and/or to use the chapter as a reference whenever you have a few 'candidate' likelihoods in your head. Reading Chapter 12 in SR will subsequently teach you to create mixtures of these likelihoods if you need further hacks such as zero inflation. Remember the YouTube series explain the math very well. So use them as a supplement!

RO...

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