Education

Geostatistics and Applied Probability Option

The Geostatistics and Applied Probability option is aimed at 3rd year students from the Ecole des Mines de Paris wishing to complete their data science skills acquired in the school's various courses.

Geostatistics aims at the quantitative study of any phenomenon, natural or human, which presents an organization in space and/or time: it is therefore an essential extension of "classic" statistical methods when the variables of interest have a spatial and/or temporal structure. Knowledge of its models and methods is essential in particular to understand the environmental phenomena linked to ecological transition.

In various fields of application (environment; climatology; energy, agricultural or mineral resources; insurance; etc.), the option chooses to give priority to the methods and thus highlight what is common to the treatment of all spatialized (georeferenced) data, beyond the language disparities inherent in the variety of fields of application. The option is thus primarily a place of meeting and privileged dialogue between students with multiple tastes and areas of interest; it is also fundamentally an opportunity to go into practice on real data sets, and to measure the distance that sometimes separates a well-mastered theory from an effective application.

Content and Activities

The option takes place over two periods of 4 and 2 weeks. It alternates lectures and practical work. Each theme is deepened by the reading and restitution in pairs of an associated research article. Regular seminars present practical uses of the methods taught in industrial or academic contexts. A week of technical visits to Provence is also planned to meet various players in the ecological, energy and digital transitions (INRAe, LSBB, CEA Cadarache, OIE laboratory of Mines Paris).

Some courses are open to outsiders (thesis students, post-docs, etc.) wishing to learn about these themes. Contact us for more informations.

Teaching is essentially divided into four blocks detailed below:

  • The first block first addresses the issues ofexploratory analysis. An introductory course inmachine learning is also dispensed.
  • The second block allows students to familiarize themselves with the geostatistical tools and techniques basics (random functions, structural analysis, estimation of parameters by method of moments and maximum likelihood, kriging, in uni and multi-varied context, Bayesian approach).
  • The third block is dedicated to the study of simulation techniques (conditional) of geostatistical models, which make it possible to characterize uncertainties in many practical problems. Some models of stochastic geometry are also discussed (point processes, Poisson lines, Boolean model), as well as deep learning methods to train generative models.
  • The fourth block covers more advanced methods: spatio-temporal modeling, data assimilation and construction of models of random functions by stochastic partial differential equation.

ATHENS “Geostatistics” week

The ATHENS Programme is aimed at carrying out intensive specialization courses, given at each member institution during one or two defined periods ("Sessions") of the academic year (November and March), enabling students to attend one of the courses offered by the network universities during 7 days. This experience, in many cases, gives students the desire to carry out studies of a longer duration (MSc and PhD levels) at an institution different from their home institution and thus facilitates exchanges between students of the major European technological institutions.

Athens Week Geostatistics (MP16)

In earth sciences, natural resource development, and environmental studies, probabilistic models are used for the prediction and the quantification of uncertainties due to sparse sampling, measurement error, or indirect observations of the phenomenon under study. As the observations cannot be considered independent in this context, standard statistical or machine learning approches are not well suited while lacking interpretability.

This course aims at giving basic elements for the mathematical modeling of regionalized phenomena by probabilistic methods. Following a general introduction and an introduction to the R software (www.r-project.org), this one-week course covers the introduction to random function models, their inference and the associated prediction methods, namely Kriging and conditional simulations.