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Bayesian Semi-parametric Models in E...

Tian, Yuan.

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Bayesian Semi-parametric Models in Extreme Value Analysis.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Bayesian Semi-parametric Models in Extreme Value Analysis./
作者:	Tian, Yuan.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
面頁冊數:	147 p.
附註:	Source: Dissertations Abstracts International, Volume: 82-02, Section: B.
Contained By:	Dissertations Abstracts International82-02B.
標題:	Statistics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28075150
ISBN:	9798662445888

Bayesian Semi-parametric Models in Extreme Value Analysis.
Tian, Yuan.

Bayesian Semi-parametric Models in Extreme Value Analysis. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 147 p.

Source: Dissertations Abstracts International, Volume: 82-02, Section: B.

Thesis (Ph.D.)--North Carolina State University, 2020.

This item must not be sold to any third party vendors.

In climate research, it is important to study the rare events of many phenomena (rainfall, wind, temperature, etc). Extreme value analysis (EVA) focuses on modeling such rare events. The modeling is usually challenging due to the limited observations. In this thesis, we study three Bayesian semiparamteric extreme value analysis models with applications to the climate research.Chapter 1 is dedicated to the spatial extremes. The max-stable process model has been proven to be useful in analyzing these spatial rare events. In this chapter, we particularly focus on the hierarchical extreme-value process (HEVP), which is a particular max-stable process that is conducive to Bayesian computing. The HEVP and all max-stable process models are parametric and impose strong assumptions including that all marginal distributions belong to the generalized extreme value family and that nearby sites are asymptotically dependent.We generalize the HEVP by relaxing these assumptions to provide a wider class of marginal distributions via a Dirichlet process prior for the spatial random effects distribution. In addition, we present a hybrid max-mixture model that combines the strengths of the parametric and semi-parametric models.We show that this versatile max-mixture model accommodates both asymptotic independence and dependence and can be fit using standardMarkov chainMonte Carlo algorithms. The utility of our model is evaluated in Monte Carlo simulation studies and application to Netherlands wind gust data.In Chapter 2, we propose a novel mixture Generalized Pareto (MIXGP) model to calibrate extreme precipitation forecasts. This model is able to describe the marginal distribution of observed precipitation and capture the dependence between climate forecasts and the observed precipitation under suitable conditions. In addition, the full range distribution of precipitation conditional on grid forecast ensembles can also be estimated. Unlike the classical Generalized Pareto distribution that can only model points over a hard threshold, our model takes the threshold as a latent parameter. Tail behavior of both univariate and bivariate models are studied. The utility of our model is evaluated inMonte Carlo simulation study and is applied to precipitation data for the US where it outperforms competing methods.In Chapter 3, we propose a single index GPD (SI-GPD) model to reanalyze the extreme precipitation forecasts. Unlike the bivariate extreme value model proposed in Chapter 2 that merely use the maximum of multiple climate forecasts as a single predictor, the SI-GPD model uses all available forecasts to improve the accuracy of modeling precipitation extremes. The proposed SI-GPD model assumes a flexible dependence between the observed precipitation and the single index of multiple climate forecasts. In order to handle the high-dimensionality of the covariates, we further extend the model to allow for sparsity.We studied the tail behavior of the model and evaluated the model performances in numerical studies. Finally, we applied the model to re-analyze the US precipitation data.

ISBN: 9798662445888Subjects--Topical Terms:

517247
Statistics.
Subjects--Index Terms:

Extreme value analysis

Bayesian Semi-parametric Models in Extreme Value Analysis.
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520 $a In climate research, it is important to study the rare events of many phenomena (rainfall, wind, temperature, etc). Extreme value analysis (EVA) focuses on modeling such rare events. The modeling is usually challenging due to the limited observations. In this thesis, we study three Bayesian semiparamteric extreme value analysis models with applications to the climate research.Chapter 1 is dedicated to the spatial extremes. The max-stable process model has been proven to be useful in analyzing these spatial rare events. In this chapter, we particularly focus on the hierarchical extreme-value process (HEVP), which is a particular max-stable process that is conducive to Bayesian computing. The HEVP and all max-stable process models are parametric and impose strong assumptions including that all marginal distributions belong to the generalized extreme value family and that nearby sites are asymptotically dependent.We generalize the HEVP by relaxing these assumptions to provide a wider class of marginal distributions via a Dirichlet process prior for the spatial random effects distribution. In addition, we present a hybrid max-mixture model that combines the strengths of the parametric and semi-parametric models.We show that this versatile max-mixture model accommodates both asymptotic independence and dependence and can be fit using standardMarkov chainMonte Carlo algorithms. The utility of our model is evaluated in Monte Carlo simulation studies and application to Netherlands wind gust data.In Chapter 2, we propose a novel mixture Generalized Pareto (MIXGP) model to calibrate extreme precipitation forecasts. This model is able to describe the marginal distribution of observed precipitation and capture the dependence between climate forecasts and the observed precipitation under suitable conditions. In addition, the full range distribution of precipitation conditional on grid forecast ensembles can also be estimated. Unlike the classical Generalized Pareto distribution that can only model points over a hard threshold, our model takes the threshold as a latent parameter. Tail behavior of both univariate and bivariate models are studied. The utility of our model is evaluated inMonte Carlo simulation study and is applied to precipitation data for the US where it outperforms competing methods.In Chapter 3, we propose a single index GPD (SI-GPD) model to reanalyze the extreme precipitation forecasts. Unlike the bivariate extreme value model proposed in Chapter 2 that merely use the maximum of multiple climate forecasts as a single predictor, the SI-GPD model uses all available forecasts to improve the accuracy of modeling precipitation extremes. The proposed SI-GPD model assumes a flexible dependence between the observed precipitation and the single index of multiple climate forecasts. In order to handle the high-dimensionality of the covariates, we further extend the model to allow for sparsity.We studied the tail behavior of the model and evaluated the model performances in numerical studies. Finally, we applied the model to re-analyze the US precipitation data.
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