In this paper we propose Bayesian and frequentist approaches to ecological inference, based on R 3 C contingency tables, including a covariate. The proposed Bayesian model extends the binomial-beta hierarchical model developed by KING, ROSEN and TANNER (1999) from the 2 3 2 case to the R 3 C case. As in the 2 3 2 case, the inferential procedure employs Markov chain Monte Carlo (MCMC) methods. As such, the resulting MCMC analysis is rich but computationally intensive. The frequentist approach, based on ®rst moments rather than on the entire likelihood, provides quick inference via nonlinear least-squares, while retaining good frequentist properties. The two approaches are illustrated with simulated data, as well as with real data on voting patterns in Weimar Germany. In the ®nal section of the paper we provide an overview of a range of alternative inferential approaches which trade-off computational intensity for statistical ef®ciency.

The enormous Nazi voting literature rarely builds on modern statistical or economic research. By adding these approaches, we find that the most widely accepted existing theories of this era cannot distinguish the Weimar elections from almost any others in any country. Via a retrospective voting account, we show that voters most hurt by the depression, and most likely to oppose the government, fall into separate groups with divergent interests. This explains why some turned to the Nazis and others turned away. The consequences of Hitler's election were extraordinary, but the voting behavior that led to it was not.

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We propose a method for analyzing possibly nonstationary time series by adaptively dividing the time series into an unknown but finite number of segments and estimating the corresponding local spectra by smoothing splines. The model is formulated in a Bayesian framework, and the estimation relies on reversible jump Markov chain Monte Carlo (RJMCMC) methods. For a given segmentation of the time series, the likelihood function is approximated via a product of local Whittle likelihoods. Thus, no parametric assumption is made about the process underlying the time series. The number and lengths of the segments are assumed unknown and may change from one MCMC iteration to another. The frequentist properties of the method are investigated by simulation, and applications to EEG and the El Niño Southern Oscillation phenomenon are described in detail.

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