Course Description
Introduction to the basics of Bayesian modeling by focusing mostly on real world applications. The course highlights the strengths of the Bayesian modeling paradigm for social science data. Topics covered include: generalized linear models, measurement models and IRT, multi-level modeling, and missing data imputation.
Athena Title
APPLIED BAYESIAN
Prerequisite
POLS 7014 or POLS 8501
Semester Course Offered
Not offered on a regular basis.
Grading System
A - F (Traditional)
Course Objectives
This course introduces the basic theoretical and applied principles of Bayesian statistical analysis in a manner geared toward students in the social sciences. The Bayesian paradigm is particularly useful for the type of data that social scientists encounter given its recognition of the mobility of population parameters, its ability to incorporate information from prior research, and its ability to update estimates as new data are observed. The course will begin with a discussion of the strengths of the Bayesian approach for social science data and the philosophical differences between Bayesian and frequentist analyses. Next, the course will cover the theoretical underpinnings of Bayesian modeling and provide a brief introduction to the primary estimation algorithms. The bulk of the course will focus on estimating and interpreting Bayesian models from an applied perspective. Students will be introduced to the Bayesian forms of the standard statistical models taught in regression and MLE courses (i.e., normal, logit/probit, Poisson, etc.). This course assumes a solid understanding of the linear model and matrix algebra and some exposure to models with limited dependent variables. The course will rely heavily on R and WinBUGS for estimation. Prior experience with these software packages is preferred but not assumed. Note: Although this course will cover some of the basics of MCMC and the Gibbs Sampler (among other sampling algorithms), application/interpretation will be the primary focus. For this reason, students already familiar with the basics of Bayesian modeling using WinBUGS, MCMC-pack, JAGS or some other software may find the Bayesian course offered in the second session more appropriate.
Topical Outline
-- Why Bayesian statistics is appropriate for the social sciences. -- Historical development. -- Why are we uncertain about probability? -- Bayes’ law and conditional probability. -- Likelihood theory and estimation review. -- Probability review. -- The generalized linear model and the link function. -- The Bayesian setup. -- What is a prior? -- Combining priors and likelihoods. -- Interpreting a posterior. -- Sampling from univariate posteriors using R. -- The Bayesian normal model. A LOT more on priors... -- Conjugacy. -- Noninformative v. informative priors. -- Uniform priors. -- Elicited priors. -- Assessing model quality and convergence. -– Using R. -– Using WinBUGS. -– Other methods. -- Interpreting and presenting Bayesian model results. -- Binary logit/probit. -- Ordered logit/multinomial logit. -- Poisson and other event count models. -- Bayesian forecasting from logit models. -- Item response theory (IRT) and ideal point estimation. -- Other latent variable/measurement/structural models. –- Models with missing data.