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Changepoint analysis is a useful tool in environmental statistics in that it provides a methodology for threshold detection and modeling processes subject to periodic changes in the underlying model due to anthropogenic effects or natural phenomena. Several applications of changepoint analysis are investigated here. The use of inappropriate changepoint detection methods is first discussed and the need for a simple, flexible, correct method is established and such a method is proposed for the mean-shift model. Data from the Everglades, Florida, USA is used to showcase the methodology in a real-world setting. An extension to the case of time-series data represented via transition matrices is presented as a result of joint work with Matt Williams (Department of Statistics, Virginia Tech) and rainfall data from Kenya, Africa is presented as a case-study. Finally the multivariate changepoint problem is addressed by a two-stage approach beginning with dimension reduction via principal component analysis (PCA). After the dimension reduction step the location of the changepoint in principal component space is estimated and assuming at most one change in a mean-shift setting, all possible sub-models are investigated. / Ph. D.

This thesis investigates how architecture engages with the natural landscape through iterative designs of exhibition space. Proposals of architecture adjacent to Smith Mountain Lake as well as along the Cascade Falls Trail in Virginia were considered. The design proposals led to a resolution that particular considerations are critical in relating architecture and nature, specifically a building's spatial organization and orientation, its materiality and tectonic assembly, and the bounding thresholds differentiating between inside and outside. / Master of Architecture / The central idea of my exploration is to engage with nature and create a building that relates to the Virginian landscape consisting of mountain, forest and water. The design exploration began with a site at Smith Mountain Lake and then a site at Cascade Falls Trail. To make the architecture, many aspects were considered - how to place the architecture in the landscape, the choice of the building's materials, how the building is constructed, the use of walls versus windows, and finally, not only creating a relationship between architecture and landscape, but also determining nuanced ways to connect the two.