This is the repository for the code related to the paper
Marco Oesting. Kirstin Strokorb. A Comparative Tour through the Simulation Algorithms for Max-Stable Processes. Statist. Sci. 37 (1) 42 - 63, February 2022. https://doi.org/10.1214/20-STS820
Previously arXiv preprint 1809.09042.
The repository consists of two folders Section2_DataExample and Section6_NumericalResults containing the code related to the corresponding sections of the paper.
The folder Section2_DataExample contains the following six files:
- DataExample.R
- DataExample_Advanced.R
- Algorithms.R
- AuxiliaryFunctions.R
- Section2.RData
- inlandBRsimu_0001.RData
DataExample.R allows to retrace all estimation and simulation steps in Section 2 ``Data Example'' of the manuscript. The actual simulation procedure used therein is part of Algorithms.R and sourced from DataExample.R. Please find a detailed description of the functions in Algorithms.R in the folder Section6_NumericalResults and the README_algorithms.txt file therein.
DataExample_Advanced.R is an extension of DataExample.R that generates several intermediate illustrative plots along the way. It relies on AuxiliaryFunctions.R and loads more R packages related to the illustration of spatial data.
Both implementations (DataExample.R and its extension DataExample_Advanced.R) load the original temperature data under investigation and some auxiliary quantities from Section2.RData.
Since the simulation of 60000 samples from the fitted max-stable process on the considered inland grid takes several days on a standard laptop, we have exemplarily included our first 600 simulations in the file inlandBRsimu_0001.RData. Thereby, the reader will be able to retrace how to obtain answers for questions Q1 and Q2 in the article as illustrated here based on these (insufficient) 600 samples.
The folder Section6_NumericalResults contains the following four files:
- Algorithms.R
- README_algorithms.txt
- Code_SimulationStudy.R
- SimulationStudy_Param.RData
The three generic simulation procedures used to obtain the numerical results are included in the file Algorithms.R. A detailed description of the functions therein is given in README_algorithms.txt.
Code_SimulationStudy.R contains sample code to recover the results of the numerical experiments for both Brown-Resnick and extremal-t processes. The input parameters for the simulation procedures in the different settings are given in SimulationStudy_Param.RData.
The file Section2.RData contains daily maximum temperatures from 1990 to 2019 that were measured at 18 inland stations in the Netherlands and are freely available from knmi.nl.
Some auxiliary functions for the simulation are taken from and parts of simulation algorithms themselves are based on the supplementary material of
C. Dombry, S. Engelke & M. Oesting (2016), Exact simulation of max-stable processes, Biometrika 103(2), pp.303-317
available from academic.oup.com.