Conditional simulation of a positive random vector subject to max-linear constraints. A geometric perspective

Christian Lantuéjoul (1) , Francis Maisonneuve (2) , Jean-Noël Bacro (3) , Liliane L. Bel (4)

1 GEOSCIENCES - Centre de Géosciences
2 École des Mines de Paris
3 UM2 - Université Montpellier 2 - Sciences et Techniques
4 MIA-Paris - Mathématiques et Informatique Appliquées

Predicting natural phenomena modeled by max-stable random fields with Fréchet margins is not simple because these models do not possess finite first and second order moments. In such situations, a Monte Carlo approach based on conditional simulations can be considered. In this paper we examine a recent algorithm set up by Wang and Stoev to conditionally simulate a max-stable random field with discrete spectrum. Besides presenting this algorithm, we provide it with a geometric interpretation and put emphasis on several implementation details to obviate its combinatorial complexity. Along the way, a number of other critical issues are mentioned that are not often addressed in the current practice of conditional simulations. An illustrative example is given.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Christian Lantuéjoul, Francis Maisonneuve, Jean-Noël Bacro, Liliane L. Bel. Conditional simulation of a positive random vector subject to max-linear constraints. A geometric perspective. Ninth International Geostatistics Congress, Jun 2012, Oslo, Norway. 6 p. ⟨hal-00766156⟩