# Suggestions for a Gentle Bayesian Statistics Tutorial

Last week I was hosted by Mike Palopoli and the Bowdoin College Biology Department, where I gave a departmental seminar on my current work on Bayesian divergence time estimation methods. Bowdoin College is a 4-year liberal arts college with some very bright undergraduates. Several of the honors biology majors attended my talk and after the seminar Mike and I led a discussion of my work and computational evolutionary biology, in general.

During this discussion I got stumped by a question from one of the students. He asked if I could recommend **a basic and gentle primer on Bayesian statistics for someone with very little statistics training**. (This particular student is currently involved in a population genetics project using Bayesian analysis.) I recommended online teaching materials from the various phylogenetics/molecular evolution workshops, including Bodega and this blog, but I couldn’t point him toward a book that I felt would be suitable for someone without a strong understanding of probability theory. As a graduate student, I took Bill Jefferys’ Bayesian Inference course at the University of Texas, where we used Bayesian Data Analysis by Gelman et al. This book is a great introduction (as was Bill’s awesome course), but might be too advanced even for a bright and motivated undergraduate biology major.

So my goal for my first post on the Treethinkers’ blog is to seek out suggestions from readers: *What is a good, introductory primer on Bayesian inference that is suitable for the undergraduate level?*

Please add your suggestions in the comments below.

Tracy HeathPost authorMy officemate, Michael Landis, recommends http://yudkowsky.net/rational/bayes, which provides interactive tools for understanding Bayes theorem. It’s a really cool tutorial.

Bob ThomsonNate Silver’s book The Signal and the Noise is pretty readable and has a very gentle introduction to Bayesian thinking. If I recall correctly, there’s no biology in it at all, but it does have lots of examples from everyday life that should be engaging for undergraduates.

edit: screwed up my link.

Brian MooreThis is a common question I get as well: “it’s been a long time since I took a math/stats course and/or the courses I took did not cover the relevant probability theory–where do I start?” Unfortunately, there is no gentle introductory text to Bayesian inference that is specific to phylogenetics (although I think there are a couple that are very close to publication). My favorite introduction to probability theory (for biologists who have little or no background) is A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution by Sally Otto and Troy Day. This is an amazingly clear and accessible introduction to the material needed to understand stochastic models and likelihood-based (ML and Bayesian) inference. Specifically, it includes three short (20–40) page ‘primers’ on functions and approximations, linear algebra, and probability theory that provide a sound basis for biologists to shed their fear of equations. Highly recommended!—Brian

Tracy HeathPost authorThese are great suggestions! I haven’t read Nate Silver’s book, but I have had conversations with other Bayesians who have and most appreciate its accessibility. It is also quite current and might be a great introduction to Bayesian thinking.

The Otto and Day book is also very good. And if you click on Brian’s link, you will notice that he searched for “mathematical moles for biology otto” on Amazon. For anyone interested in awesome moles you should probably check out this video 😉

Sergei TarasovI recommend John Kruschke’s “Doing Bayesian Data Analysis: A Tutorial with R and BUGS” http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/ that helped me a lot to understand general principles of Bayesian machinery. It starts out from introduction to the basics of probability theory gradually moving to Bayesian analysis quite thoroughly and easy explaining all required principles of statistics (I find that sometimes even too much written to explain simple things which slows down reading process). Usually, it uses non-biological examples like coin tossing to demonstrate Bayesian principles and conduct analyses, which in my view is good since such simple examples provide faster understanding of material than any other phylogeny-associated example could do. Big advantage of this book is that it contains well-commented tutorials for R with R code giving good insight on Bayesian estimation and MCMC as well as enabling to kill two birds with one stone – master Bayesian and R at the same time. I have a pdf copy of this book that I found somewhere on the web, therefore do not hesitate to send me an email and ask for the pdf if you want to have a look at this book.

Tracy HeathPost authorThank you for your suggestion, Sergei! This definitely looks like a great book. It was quite easy to find the PDF of the whole thing on the web. I can’t believe I haven’t seen this book before. Especially since I am a sucker for Bayesian inference AND golden retriever puppies.

Bob ThomsonThis book is news to me also. I’m reading through the first chapter now and it looks really great.

Mike KalishGlad someone suggested this before me — it’s the best intro book on Bayes I know of. And John is super nice, so please buy the book if you plan to use it.