Introduction to Bayesian Inference

Political scientists increasingly apply Bayesian analysis to diverse kinds of research topics, thanks to its ability to handle aggregate data without sampling processes, to analyse small-N data, and to estimate models with complex likelihood functions. The increased capacity of modern computers enables a wider range of researchers to conduct such computationally intensive estimations.

Despite these advantages there are still several points that need addressing:

• it is not sufficiently acknowledged that Bayesian statistics and conventional statistics are based on different views concerning theory and data
• the literature, including textbooks, is in general too technical to motivate most political scientists to apply Bayesian analysis to their own research questions
• the programs needed for Bayesian analysis are not user-friendly enough for most political scientists.

The course aims to close these gaps, by:

1. providing a conceptual background for Bayesian analysis
2. showing you how to read the literature using Bayesian statistics, and interpret the results
3. introducing you to software for Bayesian analysis, with political science examples.

The course covers:

• fundamentals of Bayesian analysis
• estimation of linear regression models using conjugacy and Markov Chain Monte Carlo (MCMC)
• estimation of various regression models (binary logit/probit, poisson, robust regression, etc) and further topics (model selection and check, data augmentation, etc) in Bayesian framework.

The course consists of lectures and lab sessions. The lectures deal with relevant background knowledge as well as specific skills for Bayesian analysis. In lab sessions, we will apply these skills to political and social science data. Hence, you'll also learn basic JAGS and Stan, which are necessary to conduct Bayesian estimation using MCMC.

You should have knowledge of statistical analysis including regression models with different types of dependent variables, and maximum likelihood estimation (MLE). At very least, you should know how to calculate the likelihood of certain parameter sets of a statistical model given observed data. In lab sessions we will learn how to use JAGS from R, so basic knowledge in R is also required.

This is an introductory one-week course. We cannot thoroughly treat the wide range of statistical models and further advanced topics in Bayesian statistics.

If you already have basic knowledge of Bayesian statistics and can conduct regression analysis using JAGS, do not take this course.

Statistics, including regression models with different types of dependent variables.

Maximum likelihood estimation (MLE). In particular, you should be able to distinguish likelihood.

Basic knowledge of R.