Oesting, Marco: Analysis and simulation of multivariate and spatial extremes. 2019
Inhalt
- Preface
- Contents
- Overview
- Introduction to Univariate and Spatial Extremes
- Spectral Representation of Max-Stable Processes
- Likelihood-Based Inference
- Simulation of Max-Stable Processes
- Conditional Simulation of Max-Stable Processes
- Equivalent Representations of Max-Stable Processes via ℓp Norms
- Introduction
- Generalization of the Spectral Representation
- Equivalent Representations
- Existence of ℓp Norm Based Representations
- Properties of Processes with ℓp Norm Based Representation
- Bayesian Inference for Multivariate Extreme Value Distributions
- Introduction
- Methodology
- Asymptotic Results
- Examples
- Simulation Study
- Applications in a Bayesian Framework
- Discussion
- Exact and Fast Simulation of Max-Stable Processes on a Compact Set Using the Normalized Spectral Representation
- Introduction
- Transformation of Spectral Representations
- The Optimization Problem
- Evaluating the Modified Optimization Problem
- Example: Moving Maxima Processes
- Simulation: Comparison to Other Algorithms
- Summary and Discussion
- Sampling Sup-Normalized Spectral Functions for Brown–Resnick Processes
- Introduction
- Simulating Wmax via MCMC algorithms
- Exact Simulation via Rejection Sampling
- Illustration
- Exact Simulation of Max-Stable Processes
- Introduction
- Simulation via Extremal Functions
- Simulation via the Spectral Measure
- Examples
- Complexity of the Algorithms
- Simulation on Dense Grids
- On the Distribution of a Max-Stable Process Conditional on Max-Linear Functionals
- Introduction
- General Theory
- Conditioning on One Max-Linear Functional
- Conditioning on a Finite Number of Max-Linear Functionals
- Sampling from a Max-Stable Process Conditional on a Homogeneous Functional
- Introduction
- Max-linear Models
- Extension to Conditionally Max-Linear Models
- General Max-Stable Processes
- Conclusion and Perspectives
- Diagnostics of Markov Chain in Algorithm 8.1
- Diagnostics of Markov Chain in Algorithm 8.3
- Statistical Post-Processing of Forecasts for Extremes Using Bivariate Brown–Resnick Processes with an Application to Wind Gusts
- Introduction
- Modeling by a Univariate Random Field
- Modeling by a Bivariate Random Field
- Model Fitting
- The Post-Processing Procedure
- Application to Real Data
- Bibliography