Of course, we (Robert and Gian Luca) think that the first place to start is our book Bayesian Meta-Analysis: A Practical Introduction. If there’s something that we thought you should know as a beginner in BMA, we added it to that book.
However, you will probably want to go further in reading about Bayesian methods in general, your favoured software, or meta-analysis. These are our recommendations! We have aimed for clear explanations, practical advice, and (to paraphrase Mozart) just as many mathematical formulas as are necessary.
We give links to the publishers here. If you are going to order a paper copy from elsewhere, please try to support a local, bricks-and-mortar bookshop. They can order books for you and they need your help in this day and age. Many second-hand bookshops sell through well-known online marketplaces, and that’s good too.
Crossing all of these topics, for a good general-audience overview of what statistics and machine learning are for, and how they go wrong, we suggest The Art of Statistics by David Spiegelhalter.
Bayesian methods
- Statistical Rethinking (also Richard McElreath’s lectures)
- Regression and Other Stories
- Bayesian Data Analysis
- The BUGS Book (yes, even if you don’t intend to use BUGS!)
- Uncertain Judgements
Software (not just manuals)
- The BUGS Book
- Stan User Guide (free download, there is also a Reference Manual and a Functions Manual)
- Discovering Statistics With JASP (no meta-analysis content)
- Bayesian Modelling and Computation in Python (PyMC, also free online)
Meta-analysis
- Network Meta-Analysis for Decision Making (Bayesian! includes BUGS code)
- Publication Bias in Meta-Analysis (no Bayes)
- Doing Meta-Analysis With R (also free online, one Bayesian chapter)
- Individual Participant Data Meta-Analysis (no Bayes)
- Introduction to Meta-Analysis (no Bayes)
- Cochrane handbook (online, only a bare mention of Bayes)
- Meta-Analysis in Medicine and Health Policy (plenty of interesting Bayesian ideas but this pre-dates practical software)
Our complete bibliography is also available here as a Bibtex file, please feel free to add items to your own writing.