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Title: Topological event history analysis for random fields with an application to global wind intensities
Authors: Johnson, Hollie
Issue Date: 2020
Publisher: Newcastle University
Abstract: Realisations of simulated climate variables from the CESM Large Ensemble (Kay et al., 2015) are frequently assumed to be independent and identically distributed random fields (Castruccio and Stein, 2013; Castruccio and Genton, 2014, 2016). Using concepts from the study of survival analysis and topological data analysis, we propose a methodology for the comparison of these realisations with specific application to global wind intensities. Topological data analysis is becoming more widely used as the data available in many applications grows considerably, both in volume and complexity. Where computer science and machine learning often lean heavily on clustering techniques (Gan et al., 2007; Schaef fer, 2007), TDA, and more specifically persistent homology, allows a similar analysis with greater robustness to perturbations in data, for example. We extend ideas from topo logical data analysis using an event history approach. Survival analysis has wide-ranging applications, particularly in manufacturing and medical sciences where time-to-event data is common. We are interested in how event history methods can be used as tools for the comparison of topological features in random fields. Drawing on work from these two areas of research, we consider specific topological features, connected components, on a random field and show that the number of these features differs between fields with different distributions or correlation structures. We use non parametric survival models to model the rate of emergence of such features, achieving this through a reformulation of homological births and deaths as survival events. We evaluate methods for modelling covariance of our wind intensities data on the surface of a sphere, comparing several common stationary models utilising a selection of distance measures. Our data is unusual in that we have multiple realisations of the same dataset, allowing us to examine the empirical correlation between each pair of points. We look at nonstationary approaches to modelling, including the incorporation of large-scale geo graphic descriptors, such as land, coast and ocean and consider the challenge of obtaining accurate covariance matrices on a single replicate. We demonstrate how our proposed methods are informative for the assessment of Gaus sianity in spatial data sets, comparing standard Gaussian data simulation packages. Fi nally, we apply our topological event history methods to multiple realisations from our large climate data set, identifying anomalous realisations. Keywords: survival analysis, topological data analysis, statistical topology, climate, spher ical correlation, persistent homology
Description: PhD Thesis
Appears in Collections:School of Mathematics, Statistics and Physics

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