Bayesian Ideal Point Estimation

The advantages of Bayesian methods of estimation have found application throughout political science and particularly useful in recovering the ideal point positions of legislators.  These advantages include computational efficiency of MCMC methods to jointly estimate all parameters, direct characterization of uncertainty, and simplicity of summarizing auxiliary quantities of interest.  This chapter summarizes the Bayesian ideal point model and the myriad of advances facilitated by the application of these methods.  These include addressing questions over comparability over time and chamber, the connection to executive and judicial political actors and the mass public, modelling extensions including agenda and hierarchical information, and applications involving non-roll call data.  In this discussion, future challenges are highlighted.