Bayesian statistics are a method of calculating estimates of the kinds of probabilities in which epidemiologists are often interested. We can directly estimate the probability of parameters like relative risks and odds ratios. We can predict future data values by explicitly conditioning our predictions on the existing evidence. Perhaps most compellingly, Bayesian analysis offers an attractively intuitive, yet methodologically rigorous way to update our knowledge. If our existing knowledge is scant or non-existent, and if we have a lot of data, our conclusions will be based almost entirely on the evidence at hand. But, if we have some pre-existing knowledge, say a strong intuition based on years of observation and experience, or if we’ve already conducted a number of experiments and have accumulated some results, Bayesian analysis allow us to use our knowledge. Bayesian analysis is about rational thought, and rational thought is at its core a matter of learning from observation and updating our conclusions about the world around us.

These pages consist of an introductory set of notes that includes material on Bayes’ Theorem, using probability distributions and conjugate analysis. A second set of notes on Markov Chain Monte Carlo methods and BUGS. A third (considerably longer) set of notes on linear and hierarchical modeling with BUGS, some notes on Bayesian meta-analysis, and some special topics, like approaches to missing data, working with twin or paired, data and comparing methods of clinical measurement.

As with much else on this site, these note are rife with material shamelessly taken from many very smart people. I strongly urge you to seek out the source material. In particular the excellent texts by David Spiegelhalter, Jim Alberts, John Kruschke, and Andrew Gelman, And, if you ever have the opportunity, run do not walk, to attend any class or workshop by Bendix Cartensen, Lyle Gurrin or Keith Abrams.

Despite my impeccable sources, I am certain to have introduced errors or omitted important information. I offer the material with a strong

*caveat emptor*, and only ask that if you do find my inevitable bungles, you will let me know about them.