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Advances in statistical analysis and modeling of extreme values motivated by atmospheric models and data products




Fix, Miranda J., author
Cooley, Daniel, advisor
Hoeting, Jennifer, committee member
Wilson, Ander, committee member
Barnes, Elizabeth, committee member

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This dissertation presents applied and methodological advances in the statistical analysis and modeling of extreme values. We detail three studies motivated by the types of data found in the atmospheric sciences, such as deterministic model output and observational products. The first two investigations represent novel applications and extensions of extremes methodology to climate and atmospheric studies. The third investigation proposes a new model for areal extremes and develops methods for estimation and inference from the proposed model. We first detail a study which leverages two initial condition ensembles of a global climate model to compare future precipitation extremes under two climate change scenarios. We fit non-stationary generalized extreme value (GEV) models to annual maximum daily precipitation output and compare impacts under the RCP8.5 and RCP4.5 scenarios. A methodological contribution of this work is to demonstrate the potential of a "pattern scaling" approach for extremes, in which we produce predictive GEV distributions of annual precipitation maxima under RCP4.5 given only global mean temperatures for this scenario. We compare results from this less computationally intensive method to those obtained from our GEV model fitted directly to the RCP4.5 output and find that pattern scaling produces reasonable projections. The second study examines, for the first time, the capability of an atmospheric chemistry model to reproduce observed meteorological sensitivities of high and extreme surface ozone (O3). This work develops a novel framework in which we make three types of comparisons between simulated and observational data, comparing (1) tails of the O3 response variable, (2) distributions of meteorological predictor variables, and (3) sensitivities of high and extreme O3 to meteorological predictors. This last comparison is made using quantile regression and a recent tail dependence optimization approach. Across all three study locations, we find substantial differences between simulations and observational data in both meteorology and meteorological sensitivities of high and extreme O3. The final study is motivated by the prevalence of large gridded data products in the atmospheric sciences, and presents methodological advances in the (finite-dimensional) spatial setting. Existing models for spatial extremes, such as max-stable process models, tend to be geostatistical in nature as well as very computationally intensive. Instead, we propose a new model for extremes of areal data, with a common-scale extension, that is inspired by the simultaneous autoregressive (SAR) model in classical spatial statistics. The proposed model extends recent work on transformed-linear operations applied to regularly varying random vectors, and is unique among extremes models in being directly analogous to a classical linear model. We specify a sufficient condition on the spatial dependence parameter such that our extreme SAR model has desirable properties. We also describe the limiting angular measure, which is discrete, and corresponding tail pairwise dependence matrix (TPDM) for the model. After examining model properties, we then investigate two approaches to estimation and inference for the common-scale extreme SAR model. First, we consider a censored likelihood approach, implemented using Bayesian MCMC with a data augmentation step, but find that this approach is not robust to model misspecification. As an alternative, we develop a novel estimation method that minimizes the discrepancy between the TPDM for the fitted model and the estimated TPDM, and find that it is able to produce reasonable estimates of extremal dependence even in the case of model misspecification.


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