Statistical Analysis of Lattice Data with Wavelet Variance Methods and Spatiotemporal Modeling of Infectious Disease Spread

• Main Author: Geilhufe, Marc
• Format: Doctoral or Postdoctoral Thesis
• Language: English
• Published: Universitetet i Tromsø 2013
• Subjects: VDP::Mathematics and natural science: 400::Mathematics: 410::Statistics: 412; VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Statistikk: 412; Pyramid; The Pyramid; Sea ice
• Online Access: https://hdl.handle.net/10037/5247

The papers of this thesis are not available in Munin: 1. Geilhufe, M., Percival, D. B. and Stern, H. L.: 'Two-dimensional wavelet variance estimation with application to sea ice SAR images', Computers & Geosciences (2013), vol. 54:351-360, available at http://dx.doi.org/10.1016/j.cageo.2012.11.020 2. Thon K., Geilhufe, M. and Percival, D. B.: 'A multiscale wavelet-based test for isotropy of random fields on a regular lattice' (manuscript) 3. Geilhufe, M., Held, L., Skrøvseth, S. O., Simonsen, G. S. and Godtliebsen, F.: 'Power law approximations of movement network data for modeling infectious disease spread' (manuscript) The focus of this thesis is the analysis of both regular and irregular lattice data, described in three papers. Paper I presents an extension of the pyramid algorithm for efficient Maximal Overlap Discrete Wavelet Transform coefficient calculation. As opposed to common usage of two-dimensional wavelet decomposition, it here also allows for different scales in the vertical and horizontal direction. Wavelet variances are investigated for scale-dependent analysis of spatial patterns. A practical geoscience application with Synthetic Aperture Radar images of sea ice illustrates its potential. In Paper II wavelet variances are used to develop a novel test for isotropy of random fields. Isotropy is frequently assumed in spatial modeling. It requires the covariance or variogram function of a stationary or intrinsically stationary spatial process to depend only on the distance between two locations, independent of direction. In a simulation study, the presented test for isotropy is applied to realizations of various isotropic and anisotropic Gaussian random fields. Its performance is superior compared to existing methods, both on the general applicability and the consistent rejection rate close to the nominal level for isotropic fields, while the power for anisotropic fields is comparable to or better than other methods. An example connected to the manufacturing of paper also demonstrates ...