maxLinear: an R package for conditional sampling of max-stable random fields.

Author: Yizao Wang (homepage)

Please contact Yizao for any problems.

Overview

The package focuses on the conditional sampling for max-linear models, addressed in Wang and Stoev (2011). The max-linear models cover a large class of max-stable random fields. Therefore, our package provides a computational tool for prediction on such random fields. Namely, the package produces samples from the exact conditional distribution, based on multiple obseravtions. In practice, our package can deal with max-linear models with 10000 hidden random variables and produce conditional samples of the entire random field within seconds. The examples are based on the discrete Smith model (Smith 1990, de Haan and Pereira, 2006). The core part of the package is written in C++.

Our package can also simulate the (unconditional) max-linear random fields. However, some classes of stationary max-stable random fields can be done in a different way by the package RandomFields (see Schlather 2002).
Installation

1. Download the R package installation file and

2. Install the package by the following command:

R CMD INSTALL maxLinear_1.0.tar.gz

Documentation pdf

Demos

The following commands run the two demos in R:

demo(demoSampling)

demo(demoConditionalSampling)

on sampling and conditional sampling from the Smith model.


Some plots in Wang and Stoev 2011 were produced by these codes.

(In this case, R package "fields" is required for output.)		 4 condtional samples from the de Haan-Pereira model



References
  1. Reinhard Furrer and Douglas Nychka and Stephen Sain. fields: Tools for Spatial Data, 2009, R package version 6.01. http://CRAN.R-project.org/package=fields
  2. Laurens de Haan and Teresa T. Pereira. Spatial Extremes: Models for the Stationary Case. The Annals of Statistics, Vol. 34, No. 1, 146-168. 2006.
  3. Martin Schlather. Models for Stationary Max-Stable Random Fields. Extremes 5(1), 33-44. 2002.
  4. Richard L. Smith. Max-Stable Processes and Spatial Extremes. Unpubished prepreint. 1990.
  5. Yizao Wang and Stilian A. Stoev. Conditional Sampling for Spectrally Discrete Max-Stable Random Fields. Advances in Applied Probability, Vol. 43(2), 2011, pp. 463-481. arxiv

Last updated: October 5th, 2011.