2 the Bayesian Approach

Since the early 1990s, Bayesian statistics and Markov chain Monte Carlo (MCMC) methods have become increasingly used in political science research. While the Bayesian approach enjoyed philosophical cachet up until that point, it was impractical (if not impossible) for applied work. This changed with the onset of MCMC methods, which allowed researchers to use simulation to fit otherwise intractable models. This chapter begins with an introduction to the Bayesian approach for statistical inference, contrasting it with more conventional approaches. I then introduce the Monte Carlo principle and review commonly used MCMC methods. This is followed by a practical justification for the use of Bayesian methods in the social sciences, and a number of examples from the literature where Bayesian methods have proven useful. The chapter concludes with a review of modern software for Bayesian inference, and a discussion of the future of Bayesian methods in political science. ∗This research is supported by the National Science Foundation Methodology, Measurement, and Statistics Section, Grant SES-03-50646. I acknowledge Jong Hee Park, Kyle Saunders, and seminar participants at the University of South Carolina and the University of California, Davis for their constructive comments about this chapter. R code to replicate the figures will be made available on the author’s website.