Theses and Dissertations at Montana State University (MSU)
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Item Bayesian computing and sampling design for partially-surveyed spatial point process models(Montana State University - Bozeman, College of Letters & Science, 2020) Flagg, Kenneth Allen; Chairperson, Graduate Committee: Andrew Hoegh; Andrew Hoegh and John Borkowski were co-authors of the article, 'Modeling partially-surveyed point process data: inferring spatial point intensity of geomagnetic anomalies' in the journal 'Journal of agricultural, biological, and environmental statistics' which is contained within this dissertation.; Andrew Hoegh was a co-author of the article, 'The integrated nested laplace approximation applied to spatial log-Gaussian Cox process models' submitted to the journal 'Journal of applied statistics' which is contained within this dissertation.; John Borkowski and Andrew Hoegh were co-authors of the article, 'Log-Gaussian Cox processes and sampling paths: towards optimal design' submitted to the journal 'Spatial statistics' which is contained within this dissertation.Spatial point processes model situations such as unexploded ordnance, plant and animal populations, and celestial bodies, where events occur at distinct points in space. Point process models describe the number and distribution of these events. These models have been mathematically understood for many decades, but have not been widely used because of computational challenges. Computing advances in the last 30 years have kept interest alive, with several breakthroughs circa 2010 that have made Bayesian spatial point process models practical for many applications. There is now interest in sampling, where the process is only observed in part of the study site. My dissertation work deals with sampling along paths, a standard feature of unexploded ordnance remediation studies. In this dissertation, I introduce a data augmentation procedure to adapt a Dirichlet process mixture model to sampling situations and I provide the first comparison of a variety of sampling designs with regard to their spatial prediction performance for spatial log-Gaussian Cox process (LGCP) models. The Dirichlet process model remains computationally expensive in the sampling case while the LGCP performs well with low computing time. The sampling design study shows that paths with regular spacing perform well, with corners and direction changes being helpful when the path is short.Item Visual sample plan and prior information: what do we need to know to find UXO?(Montana State University - Bozeman, College of Letters & Science, 2016) Flagg, Kenneth A.; Writing Project Advisor: Megan HiggsMilitary training and weapons testing activities leave behind munitions debris, including both inert fragments and explosives that failed to detonate. The latter are known as unexploded ordnance (UXO). It is important to find and dispose of UXO items that are located where people could come into contact with them and cause them to detonate. Typically there exists uncertainty about the locations of UXO items and the sizes of UXO- containing regions at a site, so statistical analyses are used to support decisions made while planning a site remediation project. The Visual Sample Plan software (VSP), published by the Pacific Northwest National Laboratory, is widely used by United States military contractors to guide sampling plan design and to identify regions that are likely to contain UXO. VSP has many features used for a variety of situations in UXO cleanup and other types of projects. This study focuses on the sampling plan and geostatistical mapping features used to find target areas where UXO may be present. The software produces transect sampling plans based on prior information entered by the user. After the sample data are collected, VSP estimates spatial point density using circular search windows and then uses Kriging to produce a continuous map of point density across the site. I reviewed the software's documentation and examined its output files to provide insight about how VSP does its computations, allowing the software's analyses to be closely reproduced and therefore better understood by users. I perform a simulation study to investigate the performance of VSP for identifying target areas at terrestrial munitions testing sites. I simulate three hypothetical sites, differing in the size and number of munitions use areas, and in the complexity of the background noise. Many realizations of each site are analyzed using methods similar to those employed by VSP to delineate regions of concentrated munitions use. I use the simulations to conduct two experiments, the first of which explores the sensitivity of the results to different search window sizes. I analyze two hundred realizations of the simplest site using the same sampling plan and five different window sizes. Based on the results, I select 90% of the minor axis of the target area of interest as the window diameter for the second experiment. The second experiment studies the effects of the prior information about the target area size and spatial point density of munitions items. For each site, I use four prior estimates of target area size and three estimates of point density to produce twelve sampling plans. One hundred realizations of each site are analyzed with each of the twelve sampling plans. I evaluate the analysis in terms of the detection rates of munitions items and target areas, the distances between undetected munitions items and identified areas, the total area identified, and other practical measures of the accuracy and efficiency of the cleanup effort. I conclude that the most accurate identification of target areas occurs when the sampling plan is based on the true size of the smallest target area present. The prior knowledge of the spatial point density has relatively little impact on the outcome.Item Numerical analysis of blast loaded civilian structures(Montana State University - Bozeman, College of Engineering, 2000) Lutzenberger, Bert Jeffrey