Bayesian analysis for political research

Abstract

Bayesian data analysis relies on Bayes' Theorem, using data to update prior beliefs about parameters. In this review I introduce and contrast Bayesian analysis with conventional frequentist inference and then distinguish two types of Bayesian analysis in political science. First, Bayesian analysis is used to merge historical information with current data in an analysis of likely election outcomes in Florida in 2000; particular attention is paid to the sensitivity of the results to the choice of prior (i.e., how much confidence one places in the historical information). Second, a more "modem" style of Bayesian analysis is reviewed, relying on Markov chain Monte Carlo algorithms to generate computationally intensive "random tours" of the high dimensional posterior distributions that are the focus of many contemporary Bayesian analyses; the example used is a central problem in political science, the analysis of legislators' preferences using roll call data.