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Department of Statistics

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https://hdl.handle.net/10217/100518
These digital collections include theses, dissertations, and datasets from the Department of Statistics. Due to departmental name changes, materials from the following historical department are also included here: Mathematics and Statistics.

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Browsing Department of Statistics by Subject "Bayesian statistics"

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    Statistical modeling and computing for climate data
    (Colorado State University. Libraries, 2019) Hewitt, Joshua, author; Hoeting, Jennifer A., advisor; Cooley, Daniel S., committee member; Wang, Haonan, committee member; Kampf, Stephanie K., committee member
    The motivation for this thesis is to provide improved statistical models and approaches to statistical computing for analyzing climate patterns over short and long distances. In particular, information needs for water managers motivate my research. Statistical models and computing techniques exist in a careful balance because climate data are generated by physical processes that can yield computationally intractable statistical models. Simplified or approximate statistical models are often required for practical data analyses. Critically, model complexity is moderated as much by research needs and available data as it is by computational capabilities. I start by developing a weighted likelihood that improves estimates of high quantiles for extreme precipitation (i.e., return levels) from latent spatial extremes models. In my second project, I develop a geostatistical model that accounts for the influence of remotely observed spatial covariates. The model improves prediction of regional precipitation and related climate variables that are influenced by global-scale processes known as teleconnections. I make the model more accessible by providing an R package that includes visualization, estimation, prediction, and diagnostic tools. The models from my first two projects require estimating large numbers of latent effects, so their implementations rely on computationally efficient methods. My third project proposes a deterministic, quadrature-based computational approach for estimating hierarchical Bayesian models with many hyperparameters, including those from my first two projects. The deterministic method is easily parallelizable and can require substantially less computational effort than common stochastic alternatives, like Monte Carlo methods. Notably, my quadrature-based method can also improve the computational efficiency of other recent, fast, deterministic approaches for estimating hierarchical Bayesian models, such as the integrated nested Laplace approximation (INLA). I also make the quadrature-based method accessible through an R package that provides inference for user-specified hierarchical models. Throughout my thesis, I demonstrate how improved models, more efficient computational methods, and accessible software allow modeling of large, complex climate data.