Please note: This course will be taught in hybrid mode. Hybrid delivery of courses will include synchronous live sessions during which on campus and online students will be taught simultaneously.

Ryan Bakker, from 2006-2008 was a post-doctoral fellow at the University of Oxford. From 2008-2014, he was an assistant professor at the University of Georgia. Between 2015-2019, he was associate professor and director of the Center for the Study of Global Issues at UGA. In 2019 – , he became a Reader at University of Essex. “Measuring Party Positions in Europe: The Chapel Hill Expert Survey Trend File, 199-2010”, Party Politics 21(1). “Using Bayesian Aldrich-McKelvey Scaling to Study Citizens’ Ideological Preferences and Perceptions” AJPS 59(3). “The European Common Space: Using anchoring vignettes to scale party positions across Europe” JOP 76(4). His research interests include parties and elections in the EU and Bayesian latent variable models.

Course Content:

This course introduces the basic theoretical and applied principles of Bayesian statistical analysis. The Bayesian paradigm is particularly well-suited for the types 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 begins with a discussion of the strengths and weaknesses of the Bayesian approach and the philosophical differences between the Bayesian and frequentist approaches. Most of the course content will focus on estimating and interpreting a variety of models (linear, dichotomous and polytomous choice, poisson, missing data, latent variable, and multilevel) from an applied Bayesian perspective.

Course Objectives:

Participants will learn the theoretical and empirical foundations of the Bayesian approach to statistical modelling and will leave with an improved understanding of conditional probability and mathematical statistics in general. They will also be introduced to state of the art computing tools. At the end of the course, participants will possess a suite of code that will allow them to estimate and present results for a wide-range of statistical models. The Bayesian approach is particularly useful for researchers with interests in latent variable models, multilevel models, and models with missing data.

Course Prerequisites:

Participants are expected to be well-versed in the linear model and proficient in maximum likelihood models and probability theory. Additionally, participants should have some basic understanding of derivative calculus and matrix algebra and some familiarity with R.

Representative Background Reading:

Gary King. 1986. “How Not to Lie With Statistics: Avoiding Common Mistakes in Quantitative Political Science.” American Journal of Political Science. 30, pp. 666-687.

Required Texts:

Gelman, A. and Hill, J. Data Analysis Using Regression and Multilevel/hierarchical Models. 2007. Cambridge University Press. (This book will be provided by ESS) 
Gill, Jeff, Bayesian Methods: A Social and Behavioural Sciences Approach, 3rd Edition, 2014. Chapman and Hall/CRC Statistics.

Background knowledge required

Calculus: Elementary
Linear Regression: Moderate

OLS = Moderate
Maximum Likelihood = Elementary

Computer Background
R = elementary

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 modelling 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.)as well as a variety of measurement and multilevel models. 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, MCMCpack, JAGS or some other software may find the Bayesian course offered in the second session more appropriate.

Books: The main texts for the course are: – Gelman, A. and Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press – Gill, J. (2008). Bayesian Methods: A Social And Behavioural Sciences Approach. Chapman and Hall, Boca Raton, FL For those of you unfamiliar with R, I strongly recommend:  – Jon Fox and Sandford Weisberg. An R Companion to Applied Regression. Sage, 2011.

Software: This course will rely mostly on R and WinBUGS, but will also use Stata for some applications. I strongly encourage you to install R and WinBUGS on your computers before class begins. The labs will have all necessary software as well. Both are available on line at no cost:  – – Both websites have links to documentation/user manuals for both programs and both are easily installable following the directions available on the websites. Although R and WinBUGS are not as user-friendly as many programs you may be used to (SPSS and Stata), they both use a similar language and are much more user friendly than the alternatives. That is to say, there is a learning curve for these programs, but you need not have any computer programming background to learn them rather easily-just patience and desire. See Johannes’ website for more information on JAGS.

Homework: Homework exercises will be assigned in class conditional on how far we get. We will have a ‘no child left behind’ policy. There will be between 1 and 2 assignments per week. These will be mostly computer-based with the exception of the first assignment.

Course Content: (May be modified depending on how the course progresses)

Day 1: Review of the Generalized Linear Model – Introduction, Background, and Basics of Bayesian Inference

Readings: – Gill{Chapter 1 – Siegfried, T. (2010). Odds are, it’s wrong: Science fails to face the shortcomings of statistics. Science News, 177(7):26{29.

Day 2:  Review of Probability Combining Priors and Likelihoods

Readings: – Gill{Chapter 2 – Western, B. and Jackman, S. (1994). Bayesian Inference for Comparative Research. American Political Science Review, 88(2):412{423.

Day 3: Priors

Readings: – Gill{Chapter 5 (3rd edition: 4) – Gill, J. and Walker, L. D. (2005). Elicited Priors for Bayesian Model Speciation in Political Science Research. Journal of Politics, 67(3):841{872.

HW 1 assigned: Prior and posterior distributions.

Day 4: Sampling Methods and Introduction to WinBUGS/JAGS

Readings: – Gill{Chapters 8 and 9 (3rd edition: 9 􀀀 10) - Spiegelhalter, D. J., Thomas, A., Best, N. G., and Lunn, D. (2003). WinBUGS Version 1.4 User Manual. – Plummer, M. (2011). JAGS Version 3.1.0 User Manual.

Day 5: Convergence Diagnostics

Readings: – Smith, B. J. (2007). boa: An R Package for MCMC Output Convergence Assessment and Posterior Inference. Journal of Statistical Software, 21(11):1{37.– Plummer, M. (2012). CODA manual.

HW 2 assigned: Getting familiar with WinBUGS/JAGS.

Day 6: The Normal Distribution and more on Priors

Readings: – Gill-Chapter 3 – Kerman, J. (2011). Neutral noninformative and informative conjugate beta and gamma prior distributions. Electronic Journal of Statistics, 5:1450{1470.

Day 7: The Bayesian Linear Model

Readings: – Gill{Chapter 4 (3rd edition: 5) – Efron, B. (1986). Why Isn’t Everyone a Bayesian? The American Statistician, 40(1):1{5.

HW 3 assigned: Linear model.

Day 8: Missing Data

Readings: – Jackman, S. (2000). Estimation and Inference Are Missing Data Problems: Unifying Social Science Statistics via Bayesian Simulation. Political Analysis, 8(4):307{332. http://pan.

HW 4 assigned: Debugging BUGS/JAGS code.

Day 9: Dichotomous Variable Models

HW 5 assigned: Logistic regression model.

Day 10: Measurement and IRT Models

Readings: – Fox, J.-P. and Glas, C. (2001). Bayesian Estimation of a Multilevel IRT Model Using Gibbs Sampling. Psychometrika, 66(2):271{288. – Treier, S. and Jackman, S. (2008). Democracy as a Latent Variable. American Journal of Political Science, 52(1):201{217. – Gray, J. and Slapin, J. B. (2012). How Elective are Preferential Trade Agreements? Ask the Experts. The Review of International Organizations, 7(3):309{333 – Bakker, R. (2009). Re-measuring left–right: A comparison of SEM and bayesian measurement models for extracting left–right party placements. Electoral Studies, 28(3):413–421 – Bakker, R. and Poole, K. T. (2013). Bayesian Metric Multidimensional Scaling. Political Analysis, 21(1):125–140

Hw 6 assigned: Factor Model