Nonparametric tests of spatial isotropy and a calibration-capture-recapture model
Date
2017
Authors
Weller, Zachary D., author
Hoeting, Jennifer A., advisor
Cooley, Dan, committee member
Hooten, Mevin, committee member
Ahola, Jason, committee member
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Abstract
In this dissertation we present applied, theoretical, and methodological advances in the statistical analysis of spatially-referenced and capture-recapture data. An important step in modeling spatially referenced data is choosing the spatial covariance function. Due to the development of a variety of covariance models, practitioners are faced with a myriad of choices for the covariance function. One of these choices is whether or not the covariance function is isotropic. Isotropy means that the covariance function depends only the distance between observations in space and not their relative direction. Part I of this dissertation focuses on nonparametric hypothesis tests of spatial isotropy. Statisticians have developed diagnostics, including graphical techniques and hypothesis tests, to assist in determining if an assumption of isotropy is adequate. Nonparametric tests of isotropy are one subset of these diagnostic methods, and while the theory for several nonparametric tests has been developed, the efficacy of these methods in practice is less understood. To begin part I of this dissertation, we develop a comprehensive review of nonparametric hypothesis tests of isotropy for spatially-referenced data. Our review provides informative graphics and insight about how nonparametric tests fit into the bigger picture of modeling spatial data and considerations for choosing a test of isotropy. An extensive simulation study offers comparisons of method performance and recommendations for test implementation. Our review also gives rise to a number of open research questions. In the second section of part I, we develop and demonstrate software that implements several of the tests. Because the tests were not available in software, we created the R package spTest, which implements a number of nonparametric tests of isotropy. The package is open source and available on the Comprehensive R Archive Network (CRAN). We provide a detailed demonstration of how to use spTest for testing isotropy on two spatially-referenced data sets. We offer insights into test limitations and how the tests can be used in conjunction with graphical techniques to evaluate isotropy properties. To conclude our work with spatially-referenced data in part I, we develop a new nonparametric test of spatial isotropy using the spectral representation of the spatial covariance function. Our new test overcomes some of the short-comings of other nonparametric tests. We develop theory that describes the distribution of our test statistic and explore the efficacy of our test via simulations and applications. We also note several difficulties in implementing the test, explore remedies to these difficulties, and propose several areas of future work. Finally, in part II of this dissertation, we shift our focus away from spatially-referenced data to capture-recapture data. Our capture-recapture work is motivated by methane concentration data collected by new mobile sensing technology. Because this technology is still in its infancy, there is a need to develop algorithms to extract meaningful information from the data. We develop a new Bayesian hierarchical capture-recapture model which we call the calibration-capture-recapture (CCR) model. We use our model and methane data to estimate the number and emission rate of methane sources within an urban sampling region. We apply our CCR model to methane data collected in two U.S. cities. Our new CCR model provides a framework to draw inference from data collected by mobile sensing technologies. The methodology for our capture-recapture model is useful in other capture-recapture settings, and the results of our model are important for informing climate change and infrastructure discussions.
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Subject
Google
methane
spatial statistics
isotropy
capture-recapture
R software