Theses and Dissertations at Montana State University (MSU)
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Item Retrospective analysis of a declining trumpeter swan (Cygnus buccinator) population in Yellowstone National Park(Montana State University - Bozeman, College of Letters & Science, 2021) Shields, Evan Michael; Chairperson, Graduate Committee: Jay J. RotellaBy 1933, the number of trumpeter swans (Cygnus buccinator) in the continental United States was reduced to roughly 70 individuals that nested and wintered in Yellowstone National Park (YNP) and the surrounding Greater Yellowstone area. While conservation measures saved the trumpeter swan, and their numbers have increased greatly across North America, abundance and productivity of YNP's resident trumpeter swan population declined from the 1960's through about 2010. Many hypotheses for the initial decline in YNP trumpeter swans exist, including human disturbance at nesting areas, changes in habitat quality, predation, and management of trumpeter swans outside of YNP. To improve knowledge and take advantage of long-term monitoring of trumpeter swans, this retrospective study was designed to evaluate the various competing hypotheses about possible factors associated with temporal and spatial variation in swan abundance and reproductive success in YNP for 1931-2019. Two different types of analyses were used: (1) analysis of annual park-wide counts of trumpeter swan territories with swans Absent, Present but unsuccessful (Present), and Successful, and (2) Bayesian reversible jump Markov chain Monte Carlo analysis that evaluated the utility of covariates representing swan decline hypotheses for explaining variation in annual, territory-level patterns of where swans were Absent, Present, and Successful each year. My results provide novel information on temporal patterns in the annual number of Absent, Present, and Successful territories, and analysis of covariates that are useful to explain variation in territory statuses identified several interesting covariate relationships. Swan territories within YNP were more likely to have trumpeter swans Present as opposed to Absent during 1931-2011 in years when total abundance of trumpeter swans in the broader geographic area around YNP was greater. Because several covariates have values that trend through time, it is difficult to distinguish between several alternative interpretations for the underlying causes of temporal trends. Identification of swan territories most likely to have swans Present and Successful can be a useful tool to help YNP staff manage important swan habitat or justify targeted management actions. Future work that utilizes satellite imagery to reconstruct lake/wetland hydrology is likely to be useful to describe potential changes in habitat quality.Item Statistics in the presence of cost : cost-considerate variable selection and MCMC convergence diagnostics(Montana State University - Bozeman, College of Letters & Science, 2016) Lerch, Michael David; Chairperson, Graduate Committee: Steve CherryThe overarching objective of this research is to address and recognize the cost-benefit trade-off inherent in much of statistics. We identify two places where such a balance is present for researchers: variable selection and Markov chain Monte Carlo (MCMC) sampling. An easily identifiable source of cost in science occurs when taking measurements. Researchers measure variables to estimate another quantity based on a model. When model building, researchers may have access to a large number of variables to include in the model and may consider using a subset of the variables so that future uses of the model need only measure this subset rather than all variables. The researchers are incentivized to proceed in this manner if some variables are prohibitively expensive to measure for future uses of the model. In this research, we present a new algorithm for cost-considerate variable selection in linear modeling when confronted with this problem. Since overfitting may be a danger when many variables at the disposal of the researcher, we build on the LARS and Lasso algorithms to perform cost-based variable selection in concert with model regularization. In MCMC sampling for Bayesian statistics, the cost-benefit trade-off is unavoidable. Researchers sampling from a posterior distribution must run a sampler for some number of iterations before finally stopping the sampler to make inference on the finite number of samples drawn. In this situation, the cost to be reduced is time to run the sampler while realizing the longer the sampler is run, the better the convergence. Time may not be as tangible a cost as a dollar figure, but increased wait time to perform analyses incurs the cost of running a computer and any negative effects associated with a delay as the researcher waits until the sampler has finished running. In this research, we introduce new convergence assessment tools in a diagnostic and plot. Unlike commonly used convergence diagnostics, these new tools focus explicitly on posterior quantiles and probabilities which are common inferential objectives in Bayesian statistics. Additionally, we introduce equivalence testing to the convergence assessment domain by using it as the framework of the diagnostic.Item Univel-based computational geometric modeling using high-dimensional material types with application to Monte Carlo nuclear particle transport(Montana State University - Bozeman, College of Engineering, 2015) Hall, Aaron David; Chairperson, Graduate Committee: John PaxtonComputer graphics and geometric modeling often use unstructured surface meshes to define objects. This can result in complex, time-expensive calculations to simulate surface interactions when simulating physical processes or rendering images. This thesis describes a computational geometric model based on discrete uniform-volume elements (univels), and applies this approach to well-known problem: using the Monte Carlo method to simulate the transport physics of neutral particles (neutrons and photons) through complex geometric models. The most consequential product of this work is Juniper, a comprehensive transport modeling software system useful for both practical applications and experimental research in particle transport. Using a structured Cartesian grid of univels has several promising advantages: tracking particles through a univel grid is known to be much faster than alternative geometries. And univel-based particle tracking is particularly insensitive to the complexity of the geometric model. To use these advantages Juniper must rasterize the input model into univels. Antialiasing is a well-known technique in computer graphics to reduce the visual impact of discretization artifacts. In existing graphics applications this is almost entirely done with three-dimensional color vectors. Juniper is designed to explore antialiasing the geometry univelization, while developing novel ways to cope with high-dimensionality material vectors. Antialiasing creates blended vectors near high-frequency information areas of the rasterization grid. When the grid is an image the vectors are on a three-dimensional color space and can often be stored and interpreted directly. But for particle transport the univel values are high-dimensionality material vectors. An exact representation of their blended forms yields impractically large model sizes. Instead, these vectors can be quantized to a manageable set of prototype vectors, reducing the univel grid to a table of indices. The quantized material vectors retain the computational advantages of univelized particle transport while potentially improving the fidelity of the transport results. Exploring this problem has provided new insights into digitization of high-dimensional values, effects of univel size on transport result accuracy, and the antialiasing of high-dimensional vector spaces. A new library of carefully defined high-precision cargo object models in a universal format (XML) is another result.Item Rapid geometry interrogation for a uniform volume element-based Monte Carlo particle transport simulation(Montana State University - Bozeman, College of Engineering, 1998) Frandsen, Michael WilliamItem Visualizing Monte Carlo computed radiation energy values by using a density emitter(Montana State University - Bozeman, College of Engineering, 1994) Donahue, Brett A.Item A Monte Carlo study of several regression estimators in the context of second-order autocorrelation(Montana State University - Bozeman, College of Agriculture, 1988) Zidack, Walter Ernest; Chairperson, Graduate Committee: Myles Watts.The purpose of this study is to compare the small sample properties of several estimators in the context of second-order autocorrelation by using Monte-Carlo methods. Each estimator is applied to data sets generated under several experimental design assumptions. The design assumptions consist of four structures on the independent variable, iterated over two types of error structures, with each error structure being iterated over twenty-five combinations of the autoregressive parameters evenly distributed Within the second-order autoregressive stability triangle. The four independent variable structures included: (1) white noise; (2) dampened trend; (3) growth trend; and (4) dampened cyclical trend. The error structures are generated first under the assumption that the process is stationary, and second under the assumption that the process is initially nonstationary. Each permutation of the experimental design consists of a sample size of T=25, with each permutation being replicated 2500 times. Several statistics relevant to the selection of an appropriate estimator based on efficiency, computational complexities, and inference validity of each estimator are offered. From an overall perspective of choosing an estimator that uniformly demonstrates robustness across the various independent variable types, error structure assumptions, and autoregressive parameter values, a general ranking of the estimators is apparent. The ranking of these estimators is: (1) full maximum likelihood; (2) initially nonstationary; (3) Prais-Winsten estimators; and (4) Cochrane-Orcutt estimators. Ordinary least squares, however, is the superior estimator when the distance of the point defined by the value of the autoregressive parameters is close to the center of the second-order autoregressive stability triangle. The performance of the initially nonstationary estimator is not substantially below that of the full maximum likelihood estimator when viewed from the perspective of overall performance across the various subexperimental designs. This result coupled with the ease in implementing the initially nonstationary estimator for any order autoregressive process suggests strong potential tor this estimator to efficiently estimate linear regression models with autoregressive errors.Item The small sample properties of a nonstandard estimator in the context of first order autocorrelation(Montana State University - Bozeman, College of Agriculture, 1987) Siebrasse, Paul Benjamin; Chairperson, Graduate Committee: Jeffrey T. LaFrance.The purpose of this study is to compare the small sample properties of a nonstandard estimator for first order autocorrelated errors in a time series equation with those of the more widely used estimators by using Monte Carlo experiments. The estimation method of interest arises either from the assumption that the presample residuals are not generated from an autoregressive process or from fixing the estimates of the presample values of the residuals at their unconditional expectations. This method has several nice properties. First, the estimator that is obtained is asymptotically equivalent to the standard methods. Second, the initial observations in the sample are retained, which overcomes problems that can arise in small samples when the independent variables are trended. Third, the data transformation that is used to estimate the unknown parameters of the model can be generalized to any order autoregressive process without any substantial increase in complexity. The results indicate that this nonstandard estimator performs very well relative to the other estimators considered for most experimental designs. This implies that the costs of using this more convenient estimation technique in terms of accuracy of parameter estimates is low relative to the other techniques considered.