Bayesian statistics is a branch of statistics that I have been studying recently because of the framework it provides for updating probabilities and statistical distributions with incoming data. It could prove useful to some statistical models that I am developing and will develop in the future. I've been looking for books and online material on the subject and below is a list of what I've found. I hope someone finds them useful.
There are many books on Bayesian statistical analysis, but fewer that serve as a good and comprehensive introduction to Bayesian statistics. Here's a list of some books that appear to fit that description:
- Bayesian Statistics: An Introduction, written by Peter Lee of the University of York (Lee's website has much more information on the book, including contents, problem sets, and computer codes).
- Introduction to Bayesian Statistics by William Bolstad, a senior lecturer at the University of Waikato in New Zealand. Bolstad has written a short paper on the challenges of exposing students to Bayesian statistics as opposed to classical (frequentist) statistics.
- A First Course in Bayesian Statistical Methods by Peter Hoff at the University of Washington. That book is actually available online from the Springer website, but you can only view the entire book if your institution subscribes to SpringerLink.
- Bayesian Data Analysis by Andrew Gelman, John Carlin, Hal Stern, and Donald Rubin, which appears to be a practical book that offers to give researchers the tools to apply Bayesian techniques to their data analysis.
- Bayesian Statistical Modelling by Peter Congdon. Another introductory book on the field.
I've read positive comments about the books and would love to own at least two, but I can only buy one at this time. I am leaning toward Lee's book because of the additional content of the problem sets and R computer codes. Hoff's book appears to be a good one as well and not extremely difficult to read.
Online course notes
There is a wealth of online notes and problem sets from university courses on Bayesian statistics. Most of the courses are not taught in the Statistics departments; some are taught by professors in the Public Health, Psychology, or Political Science departments, to give some examples. I think that's a good thing in that it demonstrates the power and applicability of Bayesian statistical analysis to problems in various fields.
- Applied Bayesian Statistics, from the Political Science department at University of Chicago
- Introduction to Bayesian Statistics, from the Stats department at University of Texas – Austin
- Bayesian Statistics for Engineers, from the ISyE department at Georgia Tech. Links to other Bayesian resources here.
- Statistics from Applications from MIT OpenCourseWare. The course is taught differently by various professors; some emphasize Bayesian statistics very heavily, and others cover it very minimally.
- A course on Bayesian Methods taught at Johns Hopkins University. Course notes are a little dry but very good.
- Peter Hoff's Bayesian Statistics course at University of Washington, whose material is drawn from Hoff's book. The problem sets, computer code, and datasets would be useful for anyone undertaking a self-study.
- Notes from a Bayesian Statistics short course that was taught at Université Paris Dauphine. They are very well-made but very technical and not for everyone.
There are tons of research papers on Bayesian statistical methods, but I want to highlight the tutorial papers that are available freely.
- An introductory paper on Bayesian Analysis from a course at the University of Arizona.
- A brief two-page paper in Nature Biotechnology that poses the question "What is Bayesian statistics?" and answers with a description of its main techniques, its difficulties, and its applications (focused on biotech).
- "Bayesian Statistics for Dummies", a good primer in HTML form.
- Another introduction from Mike Goddard at the University of Melbourne, with another installment of the Bayesian vs Frequentist debate.
- A concise introduction to Bayesian statistics from KP Murphy at University of British Columbia.
- Bayesian Statistics from José Bernardo at University of Valencia.
- A more advanced paper from Cooper and Herskovits on developing Bayesian networks from data.
- This guidance document from the US Food and Drug Administration focuses on best practices of Bayesian statistics for medical trials, but the information presented here can be useful for developing similar practices for sport statistics.
Of course, this is just a sample (pun not intended) of the many books and online material you can find on the subject — plenty of material that you can use for a self-study or a group study of Bayesian statistics. I hope to find more applications for it in the near future.
[Parts of this post were re-written to better organize the lists, and to add links to books and course notes. This post may be updated in the future to account for any reference material that I might find.]