Geostatistics and Data Processing

Objectives

Theory and applications of methods of analysis and data processing used in geosciences (land and space) and more broadly in engineering, such as:

• Sampling and estimation problems (of an average, a distribution)
• Regression methods (single, multiple)
• Problems of interpolation and extrapolation of data in space and time

Description

A. STATISTICAL BASIS:

• Distribution Function, Proba Density, Moments and Other Statistics
• Constructing an empirical F.d.R by points or histograms
• Estimation or adjustment of a model law (e.g., by the method of moments)
• Sampling: sampling uncertainty; Jack-Knife method
• Multivariate proba laws (attached, marginal, conditional: Bayes th)
• Variance-covariance matrix and correlation matrix
• Simple regression Y = aX + b (reinterpretation in terms of optimal estimation)

B. APPRENTICES - (depending on years and case studies):

• Multiple regression Y = A1.X1 + ... + Ak.Xk + b
• Bayesian estimation of state vectors / application to time signals
• Binary variables, random processes of failures, rare events     Delaunay Triangulation & Voronoi Polygons
• Bayesian estimation of state vectors / application in space (x, y, z): geostatistics, kriging, co-kriging

TYPES OF METHODS

"Non-statistical" methods of data analysis

• Spatial interpolation and spatial averaging by non-statistical method
• Wavelet analyzes

TYPES OF DATA

• In time (geophysical signal processing, hydroreweather, hydrological);
• In space (methods of interpolation and geostatistical estimation).

Examples:

• Time data or "signals" (time series sampled in time
• Failures, exceeding thresholds: reliability analyzes and risk studies
• Spatial data - sampled in space (x, y, z)

TYPES OF APPLICATIONS:

The case studies are drawn from earth sciences and hydrology as well as from the junction between industrial and environmental applications (construction failures, civil engineering, mining engineering, risk studies / nuclear waste management, etc.).

Bibliography

• Théorie des probabilités - Auteur : Ventsel Hélène - Editeur : Editions Mir , 1973
• Random Functions in Hydrology - Auteur : Bras R. et I.Rodriguez-Iturbe - Editeur : Dover Publications
• Probability, Random Variables, and Stochastic Processes - Auteur : Papoulis A.,S.U.Pillai - Editeur : McGrawHill , 2002
• Aide-Mémoire "Statistique et probabilités pour l'ingénieur" - Auteur : Veysseyre Renée - Editeur : Dunod , 2006

Session 1 ou session unique - Contrôle des connaissances

Session 2 - Contrôle des connaissances