Geographic Information Systems-Based Approaches to Study Congressional Redistricting in the United States

The ability for the citizens of a nation to determine their own representation has long been regarded as one of the most critical objectives of any electoral system. Without having the assurance of equality in representation, the fundamental nature and operation of the political system is severely undermined. Given the centuries of institutional reforms and population changes in the American system, Congressional Redistricting stands as an institution whereby this promise of effective representation can either be fulfilled or denied. The broad set of processes that encapsulate Congres- sional Redistricting have been discussed, experimented, and modified to achieve clear objectives and have long been understood to be important. Questions remain about how the dynamics which link all of these processes operate and what impact the real- ities of Congressional Redistricting hold for representation in the American system. This dissertation examines three aspects of how Congressional Redistricting in the Untied States operates in accordance with the principle of “One Person, One Vote.” By utilizing data and data analysis techniques of Geographic Information Systems (GIS), this dissertation seeks to address how Congressional Redistricting impacts the principle of one person, one vote from the standpoint of legislator accountability, redistricting institutions, and the promise of effective minority representation.

Advances in Dynamic Modeling and Computation for Count Data

A class of multi-process models is developed for collections of time indexed count data. Autocorrelation in counts is achieved with dynamic models for the natural parameter of the binomial distribution. In addition to modeling binomial time series, the framework includes dynamic models for multinomial and Poisson time series. Markov chain Monte Carlo (MCMC) and Po ́lya-Gamma data augmentation (Polson et al., 2013) are critical for fitting multi-process models of counts. To facilitate computation when the counts are high, a Gaussian approximation to the P ́olya- Gamma random variable is developed.

Three applied analyses are presented to explore the utility and versatility of the framework. The first analysis develops a model for complex dynamic behavior of themes in collections of text documents. Documents are modeled as a “bag of words”, and the multinomial distribution is used to characterize uncertainty in the vocabulary terms appearing in each document. State-space models for the natural parameters of the multinomial distribution induce autocorrelation in themes and their proportional representation in the corpus over time.

The second analysis develops a dynamic mixed membership model for Poisson counts. The model is applied to a collection of time series which record neuron level firing patterns in rhesus monkeys. The monkey is exposed to two sounds simultaneously, and Gaussian processes are used to smoothly model the time-varying rate at which the neuron’s firing pattern fluctuates between features associated with each sound in isolation.

The third analysis presents a switching dynamic generalized linear model for the time-varying home run totals of professional baseball players. The model endows each player with an age specific latent natural ability class and a performance enhancing drug (PED) use indicator. As players age, they randomly transition through a sequence of ability classes in a manner consistent with traditional aging patterns. When the performance of the player significantly deviates from the expected aging pattern, he is identified as a player whose performance is consistent with PED use.

All three models provide a mechanism for sharing information across related series locally in time. The models are fit with variations on the P ́olya-Gamma Gibbs sampler, MCMC convergence diagnostics are developed, and reproducible inference is emphasized throughout the dissertation.