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Advanced stochastic simulations (1 day)

Dates: July 7th (9am – 5pm)

Leaders: Christian Lantuéjoul & Thomas Romary (Mines ParisTech, France)

Christian Lantuéjoul is a research director at the Centre de Geosciences of Mines Paris-Tech. He has always been working in this institute, at fi rst in mathematical morphology with J. Serra, then in geostatistics with G. Matheron. His main elds of interest are stereology, stochastic geometry and stochastic simulation. His research concerns the design of algorithms for simulating conditionally spatial stochastic models. He is the author of a monograph “Geostatistical simulation. Models and algorithms” published by Springer.

Thomas Romary is currently a research fellow in the Geostatistics team of the Geosciences and Geoengineering center at Mines ParisTech. He received a double MSc (’05) in statistical engineering / theoretical statistics from the ENSAI (French school of statistical engineering) and the University of Rennes 2, France. He then received its PhD (’08) in Mathematics from the University of Paris 6, France. Dr. Romary’s research interests are in the area of geostatistics and spatial modeling, more specifically in design of experiments for spatial data, computational methods for large datasets, clustering of spatial data and Bayesian inverse modeling. He develops geostatistical methods for applications in geophysical and environmental science.

Description: Designing stochastic simulation algorithms is like playing with a building kit. Basic elements are gradually combined to produce more and more sophisticated algorithms. These elements include not only basics on random variables (inversion, acceptance-rejection and composition techniques), but also Markov chain techniques (Metropolis-Hastings algorithm, Gibbs sampler, sequential approach).

Their combination makes it possible to conditionally simulate random field models that can take binary (Boolean model, truncated Gaussian random field), discrete (plurigaussian random field, dead leaves model, substitution random field) or continuous values (Gaussian or max-stable random fields).

Classical as well as original algorithms will be reviewed and discussed with a particular focus on their underlying assumptions, pros and cons. A comparison will be made with stochastic imaging techniques (MPS).

This short course will also be the opportunity of discussing a number of critical issues such as the correctness of simulation algorithms and their implementation, and the variability of outcomes, that is their statistical fluctuations.

Workshop material: The material can be downloaded by clicking here.