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Gentle Introduction to Bayesian Statistics

Juraj Medzihorsky
juraj.medzihorsky@gmail.com

University of Gothenburg

Juraj Medzihorsky gained his PhD in Political Science from CEU and is currently a Postdoc at the Department of International Relations there.

His main research interests are models of election returns, modelling unobserved heterogeneity with mixtures, and text analysis.

His research has appeared in Political Analysis and PS:Political Science & Politics.

  @medzihorsky


Course Dates and Times

Thursday 28 - Saturday 30 July

10:00-12:00 and 14:00-17:00

15 hours over 3 days

Prerequisite Knowledge

The course participants should be familiar with the most common statistical models used in the social sciences. In particular, a familiarity with OLS and logistic regression is required. The participants should be familiar with R, especially with loading and manipulating data, fitting common statistical models, and plotting.


Short Outline

The course is intended for researchers familiar with the basic statistical toolbox of social science who wish to learn about Bayesian statistics. First, it exposes the differences between classical and Bayesian statistics from the perspective of applied social science research. Second, it introduces Bayesian counterparts of some of the most common statistical methods in social science. The course is designed as hands-on, with the focus on applications using existing software, specifically R and JAGS.  JAGS belongs to the BUGS family (WinBUGS, OpenBUGS etc), and allows to define custom model using a simple and straightforward language and fit them with Markov chain Monte Carlo. Consequently, the course does not include detailed discussions of algorithms used to fit Bayesian models and instruction on topics such as writing their own samplers from scratch. The participants can deepen their knowledge by taking the week-long Bayesian course offered at the WSMT, and advanced participants by taking the week-long advanced Bayesian course at the SSMT.


Long Course Outline

Day 1: What is Bayesian Statistics?

The first day of the course is dedicated to the basics of Bayesian statistics, its differences from classical (frequentist) statistics, basics of Bayesian computation using Markov chain Monte Carlo, and the basics of the JAGS modeling language. Before Bayesian topics are introduced, several topics from frequentist statistics are reviewed in order to facilitate the introduction of the Bayesian perspective. These include common probability distributions, null hypothesis significance testing and the t-test, confidence intervals, likelihood function, Normal linear regression (a.k.a. OLS), and Binomial logistic regression (a.k.a. logit). The review is not a substitute for a course on these topics. After an exposition of the basic features of Bayesian statistics a user-friendly tools for Bayesian computation—the JAGS language—will be introduced.

 

Day 2: Linear Regression and GLM

The Normal linear model regression and its relatives from the GLM family, such as the Binomial logistic regression are the workhorses of applied social science research. The second day of the course is dedicated to their Bayesian versions. The frequentist and Bayesian version of these models often produce numerically close coefficient values. However, their interpretation is different, and the Bayesian one might in many research contexts appeal more. In addition, Bayesian statistics allows to use extra-data information, e.g., from case studies or expert knowledge, which can lead to quantities that are also numerically different from those under frequentist equivalents of the models. Finally, in Bayesian statistics modeling of hierarchies is straightforward, and simple in JAGS or similar modeling languages, which will be shown on the hierarchical (or multilevel) linear model.

 

Day 3: Bayesian Model Checking and Evaluation

The final day of the course focuses on model checking and evaluation from the Bayesian perspective. The topics covered are posterior predictive checks, inspections of residuals, and goodness-of-fit measures. In Bayesian statistics, all unobserved quantities are random variables. Consequently, it is possible to compute and inspect posterior distributions not only for regression coefficients and similar quantities, but also for the individual fitted values, or fit statistics such as the R².

Day Topic Details
Thursday What is Bayesian Statistics?

2 hours seminar 3 hours lab

Friday Linear Regression and GLM

2 hours seminar 3 hours lab

Saturday Bayesian Model Checking and Evaluation

2 hours seminar 3 hours lab

Day Readings
Thursday

Jackman, S. (2004). Bayesian analysis for political research. Annu. Rev. Polit. Sci., 7, 483-505.

 

Ntzoufras, I. (2011). Bayesian Modeling Using WinBUGS. Wiley. Chapter 5.


Strongly recommended also:

Ntzoufras, I. (2011). Bayesian Modeling Using WinBUGS. Wiley. Chapters 1-2.

Friday

Ntzoufras, I. (2011). Bayesian Modeling Using WinBUGS. Wiley. Chapters 7-8.

 

Recommended also:

Ntzoufras, I. (2011). Bayesian Modeling Using WinBUGS. Wiley. Chapter 9.

Saturday

Ntzoufras, I. (2011). Bayesian Modeling Using WinBUGS. Wiley. Chapters 10.

 

Recommended also:

Gelman, A., & Hill, J. (2006). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press.  Chapter 24.

Software Requirements

R (with assorted packages available on CRAN), and JAGS.  All software is freely available and cross-platform.  The participants are strongly encouraged to install JAGS and the rjags package before the start of the course, and to contact the instructor beforehand in this manner.  The installation files for JAGS are available at http://mcmc-jags.sourceforge.net/  The rjags package provides an R interface to JAGS can be installed the usual way in R from CRAN.

Hardware Requirements

Participants need their own laptop. Any contemporary notebook computer that can run R.

Literature

Lynch, S.M. (2007). Introduction to Applied Bayesian Statistics and Estimation for Social Scientists. Springer.


Additional Information

Disclaimer

This course description may be subject to subsequent adaptations (e.g. taking into account new developments in the field, participant demands, group size, etc). Registered participants will be informed at the time of change.

By registering for this course, you confirm that you possess the knowledge required to follow it. The instructor will not teach these prerequisite items. If in doubt, please contact us before registering.