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.

Coal-fired Power Plants with Flexible Amine-based CCS and Co-located Wind Power: Environmental, Economic and Reliability Outcomes

Carbon Capture and Storage (CCS) technologies provide a means to significantly reduce carbon emissions from the existing fleet of fossil-fired plants, and hence can facilitate a gradual transition from conventional to more sustainable sources of electric power. This is especially relevant for coal plants that have a CO2 emission rate that is roughly two times higher than that of natural gas plants. Of the different kinds of CCS technology available, post-combustion amine based CCS is the best developed and hence more suitable for retrofitting an existing coal plant. The high costs from operating CCS could be reduced by enabling flexible operation through amine storage or allowing partial capture of CO2 during high electricity prices. This flexibility is also found to improve the power plant’s ramp capability, enabling it to offset the intermittency of renewable power sources. This thesis proposes a solution to problems associated with two promising technologies for decarbonizing the electric power system: the high costs of the energy penalty of CCS, and the intermittency and non-dispatchability of wind power. It explores the economic and technical feasibility of a hybrid system consisting of a coal plant retrofitted with a post-combustion-amine based CCS system equipped with the option to perform partial capture or amine storage, and a co-located wind farm. A techno-economic assessment of the performance of the hybrid system is carried out both from the perspective of the stakeholders (utility owners, investors, etc.) as well as that of the power system operator.

In order to perform the assessment from the perspective of the facility owners (e.g., electric power utilities, independent power producers), an optimal design and operating strategy of the hybrid system is determined for both the amine storage and partial capture configurations. A linear optimization model is developed to determine the optimal component sizes for the hybrid system and capture rates while meeting constraints on annual average emission targets of CO2, and variability of the combined power output. Results indicate that there are economic benefits of flexible operation relative to conventional CCS, and demonstrate that the hybrid system could operate as an energy storage system: providing an effective pathway for wind power integration as well as a mechanism to mute the variability of intermittent wind power.

In order to assess the performance of the hybrid system from the perspective of the system operator, a modified Unit Commitment/ Economic Dispatch model is built to consider and represent the techno-economic aspects of operation of the hybrid system within a power grid. The hybrid system is found to be effective in helping the power system meet an average CO2 emissions limit equivalent to the CO2 emission rate of a state-of-the-art natural gas plant, and to reduce power system operation costs and number of instances and magnitude of energy and reserve scarcity.