Official Description: This course is a PhD-level introduction to the Big Three frontiers of 21st century model-based statistical inference: (1) Bayesian inference and Markov chain Monte Carlo (MCMC) estimation, (2) Mixed/hierarchical/multilevel generalized linear models (GLMM’s), and (3) formal model comparison using metrics like AIC, BIC and DIC. Each of these frontiers is intimately related to the others, and so it makes sense to teach them together. The alternative is to perpetuate the farrago of classical statistics. Having suffered through that farrago myself, I don’t wish it upon anyone else.
The course starts by focusing on “non-Bayesian” statistical inference relying upon maximum likelihood, but using Bayesian justifications and interpretations. Bayesian statistics is usually thought of as an advanced topic, completely divorced from what is usually known as “statistics.” This is a shame. It is easier to teach statistical inference with a Bayesian foundation. So I adopt a Bayesian framing at the start here, to make the course easier, not harder. Near the end of the course, when we meet some of the useful things that prior probability can do for us, it won’t seem ad hoc or magical. Bayes has been there all along.
The practical goals of the course are to teach students how to specify, fit and interpret GLM’s (generalized linear models) and GLMM’s (generalized linear mixed models), use AIC, understand how MCMC estimation works, and appreciate the powerful things Bayesian probability thinking can do for us. Some students will want to go deeper into MCMC afterwards, while others will work with GLMM’s or move on to GAM’s (generalized additive models) or PGLMM’s (phylogenetic GLMM’s), while others will want to investigate information theory or informative priors or Maxent. Of course you can’t know when you will need to pick up a new skill later in your career, so I want to provide a foun- dation that will help you grow at your own pace throughout your scientific lifetime.
Instructors: Richard McElreath
Other info and comments: The instructor is no longer at UC Davis, but the class lives on. All course lectures and materials are available on the web, so one can audit the course electronically. All of the class resources are available here. You will need a password to access some of them. You can get the password on this page, which is only accessible to those who have demonstrated an affiliation with EGSA by logging in to this site.
Course syllabus here
Software used: R
Other labels: ANT298, ECL298