Welcome to the special issue of Political Analysis dedicated to Bayesian methods. We hope that you enjoy the varied and interesting contributions herein featuring Bayesian statistical methods. For many people in empirical political science, Bayesian statistics seems like a weird offshoot of probability that surfaces occasionally in journals and books but does not occupy a particularly central role. This perception appears to be changing. In fact, it appears to be changing quite rapidly. The purpose of this issue is to support and accelerate this momentum by further demonstrating the full flexibility and power of Bayesian methodology.

Many situations exist in which a latent construct has both ordinal and continuous indicators. This presents a problem for the applied researcher because standard measurement models are not designed to accommodate mixed ordinal and continuous data. I address this problem by formulating a measurement model that is appropriate for such mixed multivariate responses. This model unifies standard normal theory factor analysis and item response theory models for ordinal data. I detail a Markov chain Monte Carlo algorithm for model fitting. I apply the model to cross-national data on political-economic risk and find that the model works well. Software for fitting this model is publicly available in the MCMCpack (Martin and Quinn 2004, “MCMCpack 0.4–8”) R package.

Political relationships often vary over time, but standard models ignore temporal variation in regression relationships. We describe a Bayesian model that treats the change point in a time series as a parameter to be estimated. In this model, inference for the regression coefficients reflects prior uncertainty about the location of the change point. Inferences about regression coefficients, unconditional on the change-point location, can be obtained by simulation methods. The model is illustrated in an analysis of real wage growth in 18 OECD countries from 1965–1992.

We fit a multilevel logistic regression model for the mean of a binary response variable conditional on poststratification cells. This approach combines the modeling approach often used in small-area estimation with the population information used in poststratification (see Gelman and Little 1997, Survey Methodology 23:127–135). To validate the method, we apply it to U.S. preelection polls for 1988 and 1992, poststratified by state, region, and the usual demographic variables. We evaluate the model by comparing it to state-level election outcomes. The multilevel model outperforms more commonly used models in political science. We envision the most important usage of this method to be not forecasting elections but estimating public opinion on a variety of issues at the state level.

In political science and related disciplines in the social and behavioral sciences, there exists an unfortunate de facto divide between qualitative and quantitative empirical research. Sometimes this divide is purely a function of training and disciplinary socialization, but often it reflects a valid dispute over the philosophical foundations of inquiry. I argue here that the Bayesian approach to quantitative empirical modeling is an amenable starting point for building a rapprochement between qualitative and quantitative research, and I introduce as an example a straightforward model that allows for the Bayesian estimation of the difference between means of very small samples with unknown and possibly unequal variances. I then extend this approach to consider nonnormal variates, informative priors, and a multivariate test of the difference of means useful for the researcher who is interested in determining whether two small samples are different on several dimensions simultaneously.

What do we really know about applicants to graduate school? How much information is in an applicant's file? What do we learn by having graduate admissions committees read and score applicant files? In this article, I develop a statistical model for measuring applicant quality, combining the information in the committee members' ordinal ratings with the information in applicants' GRE scores. The model produces estimates of applicant quality purged of the influence of committee members' preferences over ostensibly extraneous applicant characteristics, such as gender and intended field of study. An explicitly Bayesian approach is adopted for estimation and inference, making it straightforward to obtain confidence intervals not only on latent applicant quality but over rank orderings of applicants and the probability of belonging in a set of likely admittees. Using data from applications to a highly ranked political science graduate program, I show that there is considerable uncertainty in estimates of applicant quality, making it impossible to make authoritative distinctions as to quality among large portions of the applicant pool. The multiple rater model I develop here is extremely flexible and has applications in fields as diverse as judicial politics, legislative politics, international relations, and public opinion.

Multimodal, high-dimension posterior distributions are well known to cause mixing problems for standard Markov chain Monte Carlo (MCMC) procedures; unfortunately such functional forms readily occur in empirical political science. This is a particularly important problem in applied Bayesian work because inferences are made from finite intervals of the Markov chain path. To address this issue, we develop and apply a new MCMC algorithm based on tempered transitions of simulated annealing, adding a dynamic element that allows the chain to self-tune its annealing schedule in response to current posterior features. This important feature prevents the Markov chain from getting trapped in minor modal areas for long periods of time. The algorithm is applied to a probabilistic spatial model of voting in which the objective function of interest is the candidate's expected return. We first show that such models can lead to complex target forms and then demonstrate that the dynamic algorithm easily handles even large problems of this kind.