  In the United States as in other countries, political and economic divisions
cut along geographic and demographic lines. Richer people are more likely to
vote for Republican candidates while poorer voters lean Democratic; this is
consistent with the positions of the two parties on economic issues. At the
same time, richer states on the coasts are bastions of the Democrats, while
most of the generally lower-income areas in the middle of the country strongly
support Republicans. During a research project lasting several years, we
reconciled these patterns by fitting a series of multilevel models to perform
inference on geographic and demographic subsets of the population. We were
using national survey data with relatively small samples in some states, ethnic
groups and income categories; this motivated the use of Bayesian inference to
partially pool between fitted models and local data. Previous, non-Bayesian
analyses of income and voting had failed to connect individual and state-level
patterns. Now that our analysis has been done, we believe it could be
replicated using non-Bayesian methods, but Bayesian inference helped us crack
the problem by directly handling the uncertainty that is inherent in working
with sparse data.
