Browsing by Author "Fosdick, Bailey K., committee member"
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Item Open Access Improved inference in heteroskedastic regression models with monotone variance function estimation(Colorado State University. Libraries, 2018) Kim, Soo Young, author; Wang, Haonan, advisor; Meyer, Mary C., advisor; Fosdick, Bailey K., committee member; Opsomer, Jean D., committee member; Luo, J. Rockey, committee memberThe problems associated with heteroskedasticity often lead to incorrect inferences in a regression model, especially when the form of the heteroskedasticity is obscure. In this dissertation, I present methods to estimate a variance function in a heteroskedastic regression model where the variance function is assumed to be smooth and monotone in a predictor variable. Maximum likelihood estimation of the variance function is derived under normal or double-exponential error distribution assumptions based on regression splines and the cone projection algorithm. A penalized spline estimator is also introduced, and the estimator performs well when there exists a spiking problem at a boundary of domain. The convergence rates of the estimated variance functions are derived, and simulations show that it tends to be closer to the true variance function in a variety of scenarios compared to the existing method. The estimated variance functions from the proposed methods provide improved inference about the mean function, in terms of a coverage probability and an average length for an interval estimate. The utility of the method is illustrated through the analysis of real datasets such as LIDAR data, abalone data, California air pollution data, and U.S. temperature data. The methodology is implemented in the R package cgam. In addition to the variance function estimation method, the hypothesis test procedure of a smooth and monotone variance function is discussed. The likelihood ratio test is introduced under normal or double-exponential error distribution assumptions. Comparisons of the proposed test with existing tests are conducted through simulations.Item Open Access Statistical models for dependent trajectories with application to animal movement(Colorado State University. Libraries, 2017) Scharf, Henry R., author; Hooten, Mevin B., advisor; Cooley, Daniel S., committee member; Fosdick, Bailey K., committee member; Hobbs, N. Thompson, committee memberIn this dissertation, I present novel methodology to study the way animals interact with each other and the landscape they inhabit. I propose two statistical models for dependent trajectories in which depedencies among paths arise from pairwise relationships defined using latent dynamic networks. The first model for dependent trajectories is formulated in a discrete-time framework. The model allows researchers to make inference on a latent social network that describes pairwise connections among actors in the population, as well as parameters that govern the type of behavior induced by the social network. The second model for dependent trajectories is formulated in a continuous-time framework and is motivated primarily by reducing uncertainty in interpolations of the continuous trajectories by leveraging positive dependence among individuals. Both models are used in applications to killer whales. In addition to the two models for multiple trajectories, I introduce a new model for the movement of an individual showing a preference for areas in a landscape near a complex-shaped, dynamic feature. To facilitate estimation, I propose an approximation technique that exploits of locally linear structure in the feature of interest. I demonstrate the model for the movement of an individual responding to a dynamic feature, as well as the approximation technique, in an application to polar bears for which the changing boundary of Arctic sea ice represents the relevant dynamic feature.Item Open Access The social process of knowledge creation in science(Colorado State University. Libraries, 2019) Love, Hannah Beth, author; Cross, Jennifer E., advisor; Fosdick, Bailey K., committee member; Nowacki, Jeffrey, committee member; Carolan, Michael, committee memberThe Science of Team Science (SciTS) emerged as a field of study because 21st Century scientists are increasingly charged with solving complex societal and environmental challenges. This shift in the complexity of questions requires a shift in how knowledge is created. To solve the complex societal health and environmental challenges, scientific disciplines will have to work together, innovate new knowledge, and create new solutions. It is impossible for one person or one discipline to have the quantity of knowledge needed to solve these types of problems. Tackling these problems requires a team. My dissertation articles report on how knowledge is built and created on a spectrum of scientific teams from university students to long-standing teams. Collectively they answer: how is knowledge creation a social process? To answer this question, my dissertation used a mixed-methods approach that included: social network analysis, social surveys, participant observation, interviews, document analysis, and student reflections. The most important finding from my dissertation was that social relations and processes are key to knowledge creation. Historically, knowledge acquisition and creation have been thought of as individual tasks, but a growing body of literature has framed knowledge creation as a social product. This is a fundamental shift in how knowledge is created to solve complex problems. To work with scientists from other disciplines, individuals must develop personal mastery and build the necessary capacities for collaboration, collective cognitive responsibility, and knowledge building. Complex problems are solved when scientists co-evolve with teams, and individual knowledge and capacity grows alongside the ability for "team learning" Knowledge, then, is a collective product; it is not isolated or individual, but constructed and co-constructed through patterns of interactions.