I never cease to be amazed by how useful Twitter can be. I’ve recently asked for introductory resources on Bayesian inference and almost immediately got a number of great suggestions. My goal was to find materials that would be accessible to a colleague who has a standard graduate psychology training (i.e., not a huge amount of quantitative background). Twitter comments often don’t get the attention they deserve, either because they disappear into the ether of Twitter’s absurd conversation thread GUI, or because they quickly get drowned out by the latest current-events retweet storm. So I figured I’d put up a roundup of some of the materials I got, in case anyone else found them useful.

This blog post by Rob Mealey gently walks us through the example of inference on a binomial proportion, which besides being a standard example also happened to be exactly the case the colleague in question was interested in. I also liked this Shiny app by Mike Meredith, which lets you turn the various knobs of the Beta-Binomial model and see how they affect the posterior.

Another resource is the freely available first chapter in an upcoming textbook by John Winn and Chris Bishop; this chapter illustrates Bayesian inference using a murder mystery, surely an improvement over biased coins. The first chapter in the freely available Bayesian Methods for Hackers covers similar ground (in an IPython notebook!).

Shravan Vasishth shared a great set of slides from a course he gave at ESSLLI a couple of years ago, which was geared towards analyzing linguistic and psycholinguistic data. Bruno Nicenboim and Shravan have recently written a tutorial illustrating how a Bayesian analysis of data from a typical psycholinguistic experiment would work; this is somewhat more involved than what my colleague was looking for, but I personally found it very useful!

Several people suggested John Kruschke’s textbook Doing Bayesian Data Analysis, in particular chapters 4 and 5 which introduce the basic concepts of Bayesian inference. Two other textbooks that people recommended were Richard McElreath’s Statistical Rethinking (also reportedly gentle on the math) and Peter Hoff’s A First Course in Bayesian Statistical Methods. None of these textbooks are freely available online, as far as I can tell.

Let me know in the comments if there’s anything my Twitter followers missed (doubtful, but technically possible).

[Updates:

- Tristan Mahr shared some slides with relevant links. A lot of overlap with what I’ve listed above, but also some new stuff. In particular, Alexander Etz’s post How to become a Bayesian in eight easy steps looks useful if you want to dig a bit deeper. (By the way, the slides are from a tutorial on RStanARM, a package that lets you specify Bayesian regression models as R formulas and compile them into Stan – awesome idea!)
- Michael Franke has another great collection of resources, including slides from a recent minicourse on Bayesian statistics for cognitive modeling.]

Lynch’s book is fantastic if you know some calculus.

For people seriously into Bayes, also read Box and Tiao and of course Gelman et al BDA.

Lunn et al 2012 The BUGS book is truly amazing.

From my lab, take a look at

Intro to LMMs in Stan:

http://www.ling.uni-potsdam.de/~vasishth/statistics/BayesLMMs.html

Lecture notes on BDA:

https://github.com/vasishth/Statistics-lecture-notes-Potsdam/tree/master/AdvancedDataAnalysis

Fairly involved example of LMMs in Stan:

https://github.com/vasishth/RePsychLing