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In this dissertation, a variable selection method for spatial data is developed. It is assumed that the spatial process is non-stationary as a whole but is piece-wise stationary. The pieces where the spatial process is stationary are called regions. The variable selection approach accounts for two sources of correlation: (1) the spatial correlation of the data within the regions, and (2) the correlation of adjacent regions. The variable selection is carried out by including indicator variables that characterize the significance of the regression coefficients. The Ising distribution as prior for the vector of indicator variables, models the dependence of adjacent regions. We present a case study on brook trout data where the response of interest is the presence/absence of the fish at sites in the eastern United States. We find that the method outperforms the case of the probit regression where the spatial field is assumed stationary and isotropic. Additionally, the method outperformed the case where multiple regions are assumed independent of their neighbors. / Ph. D.

Modelling neuronal interactions using a directed network can be used to provide insight into the activity of the brain during experimental tasks. Magnetoencephalography (MEG) allows for the observation of the fast neuronal dynamics necessary to characterize the activity of sources and their interactions. A network representation of these sources and their connections can be formed by mapping them to nodes and their connection strengths to edge weights. Dynamic Causal Modelling (DCM) presents a Bayesian framework to estimate the parameters of these networks, as well as the ability to test hypotheses on the structure of the network itself using Bayesian model comparison. DCM uses a neurologically-informed representation of the active neural sources, which leads to an underdetermined system and increased complexity in estimating the network parameters. This work shows that inform- ing the MEG DCM source location with prior distributions defined using a MEG source localization algorithm improves model selection accuracy. DCM inversion of a group of candidate models shows an enhanced ability to identify a ground-truth network structure when source-localized prior means are used. / Master of Science

In an era of global-scale climate change, agricultural production faces a unique challenge due to its reliance on stochastic natural endowments, including temperature, precipitation, and water availability for irrigation. This dissertation presents a series of essays to examine how agricultural producers react and adapt to challenges presented by climate change and scarce irrigation water allocated through the prior appropriation doctrine. The dissertation approaches the problem from three distinct perspectives: institutional differences, climate and water availability, as well as producers' expectation on future endowments. Chapter 2 presents an institutional perspective, in which I investigate how different water allocation mechanisms within the prior appropriation doctrine result in differences in producers' crop allocation decisions. I find that water users in irrigation districts are able to plant more water-intensive crops than farmers outside irrigation districts. Chapter 3 presents the interaction between nature and human systems, in which I examine how the physiological complementarity of temperature and water availability diffuses from crop yield (at the intensive margin) to crop allocation strategies (at the extensive margin). Using a theoretical model I show that the observed complementarity reflects a combination of two mechanisms: yield impact through physiological complementarity, and adaptation response through shifting crop allocation patterns. Using an empirical model, I find that farmers adapt to changing climate conditions by growing more profitable crop mixes when presented with more growing degree-days (GDD), precipitation and groundwater access. Chapter 4 presents a behavioral perspective, in which I test how producers' expectation formation processes lead to short term over-adjustments to weather and water availability fluctuations. Using a fixed-effect regression on lagged weather and water realizations, I find that agricultural producers engage in a combination of cognitive biases, including the availability heuristic and the reinforcement strategy. Adopting these alternative learning mechanisms causes farmers to significantly over-react to more recent fluctuations in weather and water availability when making ex ante acreage and crop allocation decisions. / Ph. D. / In an era of global-scale climate change, agricultural production faces a unique challenge due to its reliance on variable natural factors, including temperature, precipitation, and water availability for irrigation. This dissertation presents a series of essays to examine how agricultural producers react and adapt to challenges presented by climate change and scarce irrigation water allocated through the prior appropriation doctrine. Chapter 2 presents an institutional perspective, in which I investigate how different water allocation regimes result in differences in producers’ cropping decisions. I find that irrigation districts benefit its users by allowing them to plant more water-intensive crops than farmers outside irrigation districts. Chapter 3 presents a natural science perspective, in which I examine how temperature and water availability jointly affect agricultural production and adaptation. I find that farmers significantly adapt to changing climate conditions by growing more profitable crop mixes when presented with higher temperature, precipitation, and groundwater access. Chapter 4 presents a behavioral perspective, in which I test how agricultural decision making are affected by how producers form expectations over future climate. I find that agricultural producers engage in a combination of cognitive biases when forming expectations, and as a result over-react to more recent fluctuations in weather and water availability when making acreage and crop allocation decisions.

This research aims to develop a process for eliciting expert knowledge and incorporating this knowledge as prior distributions for a Bayesian logistic regression model. This work was motivated by the need for less data reliant methods of modelling species habitat distributions. A comprehensive review of the research from both cognitive psychology and the statistical literature provided specific recommendations for the creation of an elicitation scheme. These were incorporated into the design of a Bayesian logistic regression model and accompanying elicitation scheme. This model and scheme were then implemented as interactive, graphical software called ELICITOR created within the BlackBox Component Pascal environment. This software was specifically written to be compatible with existing Bayesian analysis software, winBUGS as an odd-on component. The model, elicitation scheme and software were evaluated through five case studies of various fauna and flora species. For two of these there were sufficient data for a comparison of expert and data-driven models. The case studies confirmed that expert knowledge can be quantified and formally incorporated into a logistic regression model. Finally, they provide a basis for a thorough discussion of the model, scheme and software extensions and lead to recommendations for elicitation research.

The use of a finite mixture of normal distributions in model-based clustering allows to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by imposing constraints on the model or by using post-processing procedures. Within the Bayesian framework we propose a different approach based on sparse finite mixtures to achieve identifiability. We specify a hierarchical prior where the hyperparameters are carefully selected such that they are reflective of the cluster structure aimed at. In addition, this prior allows to estimate the model using standard MCMC sampling methods. In combination with a post-processing approach which resolves the label switching issue and results in an identified model, our approach allows to simultaneously (1) determine the number of clusters, (2) flexibly approximate the cluster distributions in a semi-parametric way using finite mixtures of normals and (3) identify cluster-specific parameters and classify observations. The proposed approach is illustrated in two simulation studies and on benchmark data sets.

Undergraduate enrollment in colleges and universities has grown and changed drastically over the past 2 decades, with a significant portion of this growth coming from the increased number of nontraditional students who have made the decision to make their way onto college and university campuses to pursue a college degree. Due to these changes, many institutions of higher education have had to rethink the way they have historically operated. In an attempt to better meet the needs and demands of adult nontraditional students, colleges and universities have reviewed their existing programs and instituted programs that allow for the awarding of academic credit for prior learning. For those institutions of higher education involved in the prior learning assessment (PLA) process and interested in providing a quality program, an increased emphasis and focus should be on the importance of determining what a learning activity is, and more importantly, what constitutes college-level learning. This study focused on the identification and profiling of prior learning assessment (PLA) processes in Texas public universities offering nontraditional baccalaureate degree programs, the identification of commonalties among such programs, and the determination of program quality based on established standards. The instrument utilized in this study was designed on Urban Whitaker's 10 Standards of Good Practice. The population consisted of those public institutions of higher education in Texas that offer the Texas CIP code 30.9999.40 - Applied Arts and Sciences - baccalaureate degree. A within-stage mixed-model methodology was used. Open-ended questions were used to strengthen the data obtained from the quantitative portion. This research study suggests that, although there are similarities with regards to the types of PLA processes used in the awarding of PLA credit, many of the organizations could benefit from an evaluation of their current policies, procedures, and/or common practices related to the process of awarding credit via prior learning assessment as they relate to overall quality.