Syllabus for Bayesian Statistics

Jeff Rouder
212D McAlester

There is probably no more controversial and misunderstood subject in statistics than Bayesian analysis. Fifty years ago, no statistician was trained in Bayesian methods; today Bayesian statistics is required for a PhD. Today Bayesian analysis comprises a large share of the academic statistics articles, and is well funded and preferred at the federal funding level. Bayesian analysis is also becoming more accepted in a number of fields, and is the standard in climatology and biostatistics. In the social sciences, however, it is still a subordinate modality of inquiry. Adoption is slowed because Bayesian analysis is fundamentally different than conventional analysis, and it requires the analyst to rethink and redefine foundational meanings of variability and probability.

Those of us who are Bayesian note two distinct advantages compared to conventional analysis. First, from a practical point of view, many problems that are intractable from a frequentist point of view are tractable from a Bayesian point of view. The opposite does not hold; therefore, more problems may be solve from a Bayesian perspective. Second, Bayesians argue that the philosophical underpinnings are superior, and the offered quantities better serve scientific inquiries than their conventional counterparts.

This is a new course for me and I am not sure what I will cover. Assuredly, I will teach the basics: Subjective probability, priors, posteriors, Bayes factors, etc. I will also teach Bayesian computational techniques including various MCMC methods. I will teach hierarchical models, for which Bayesian analysis is far more convenient than conventional counterparts. More to follow....

I am requesting that you have taken graduate-level regression and ANOVA. I am, however, treating the class as if you don't remember too much of the experience. I will start at the beginning and keep the course as self-contained as possible.

We will be using R. R is available for free at R is a great program. I find it to be indispensable because it is more flexible than SPSS, SAS, or Systat. It is a programming language rather than a menu-driven system (much like SAS). The big advantage over SAS is its ability to work interactively. R is so cool that it has spawned a number of R evangelists. It is a lifelong tool that will be around for many decades. The main drawback is that the learning curve is nontrivial. You will have to work a bit at it. We will also be using JAGS, which is a modern package for R for doing MCMC analysis. In contrast to R, which I know well, I dont't know JAGS. This course will give us the opportunity to learn it together.

The is a graduate elective. You and I are here because we have interest in the material. I see no point in using grades for evaluation. Therefore, I will give everyone an A for the course as long as people do their best on the homework assignments. Your grade will be based on your participation and performance on assignments. Almost all of your assignments will be based on simulation and analysis of problems. Homework will be assigned weekly or biweekly. You can ask/consult/help each other with homework to some reasonable degree (it does nobody any good if some of you turn into doers and others turn into scribes). Contact me if you are having persistent or deep problems with a homework. Homework is due at the start of class on the due date (no exceptions), and you will self grade your homework in class and turn it in.

Jackman (2009), Bayesian Analysis for the Social Sciences. The dude seems sharp and it seems much better written than competitors. It is a bit advanced, and I will be simplifying it at times in class. I will teach the concepts that he assumes (integrals, density functions, etc.).

I'll post my materials on the internet. You will bring your completed assignments to class and we will all go over them together.

Other Stuff

I would greatly prefer an interactive, fun class. Please attend, share, and help shape the class.
I do take the material fairly seriously so I might shout ``wrong'' at you. Don't take it too personally, its part of my New York heritage. I will try not to swear too much; but don't be surprised if I use cuss words to convey subtle points.

The Provost requests certain statements in a syllabus and you have seen them before. DISABILITIES: If you have any issue or concern that affects your ability to get the most out of my course, including those of disability, injury, or illness, then please come see me. ACADEMIC HONESTY: this class is a collaborative effort. It is more like group research than a class. We are all responsible that everybody learns. So, do your best to help you and your fellow classmates. Do engage the material, however, as best you can before seeking help. INTELLECTUAL PLURALISM: The University, in its limited wisdom, has a web site where you may complain if you think there is not sufficient intellectual pluralism in a course ( AUDIO/VIDEO RECORDINGS: University of Missouri System Executive Order No. 38 lays out principles regarding the sanctity of classroom discussions at the university. The policy is described fully in Section 200.015 of the Collected Rules and Regulations. In this class, students may not make audio or video recordings of course activity, except students permitted to record as an accommodation under Section 240.040 of the Collected Rules. All other students who record and/or distribute audio or video recordings of class activity are subject to discipline in accordance with provisions of Section 200.020 of the Collected Rules and Regulations of the University of Missouri pertaining to student conduct matters. Those students who are permitted to record are not permitted to redistribute audio or video recordings of statements or comments from the course to individuals who are not students in the course without the express permission of the faculty member and of any students who are recorded. Students found to have violated this policy are subject to discipline in accordance with provisions of Section 200.020 of the Collected Rules and Regulations of the University of Missouri pertaining to student conduct matters.

Research Methods 3020