# Coursebooks

## Spatial statistics

#### Lecturer(s) :

Ginsbourger David

English

#### Summary

In this course we will focus on stochastic approaches for modelling phenomena taking place in multivariate spaces. Our main focus will be on random field models and on statistical methods for model-based spatial statistics.

#### Content

In this course we will focus on stochastic approaches for modelling phenomena taking place in multivariate spaces. Our main focus will be on random field models and on statistical methods for model-based spatial statistics. Starting from generalities on random fields, we will subsequently cover topics in spatial interpolation, analysis and simulation of random field paths, model selection and parameter inference, as well as experimental design. Potential additional topics include point pattern analysis and multiple-point statistics simulation. A tentative schedule follows:

• Introduction to random fields
• Definition, construction and examples
• Notions of stationarity, continuity/differentiability, etc.
• Variography and related topics
• Spatial prediction
• Best Linear Unbiased Prediction / Simple Kriging
• The Gaussian case: interpretation and (conditional) simulation
• Parameter estimation and extensions of Kriging
• On path properties and decompositions of random fields
• General results on path continuity/differentiability
• Reproducing Kernel Hilbert Spaces ane the Loève isometry
• Advanced results on Gaussian random fields
• Topics in experimental design
• Static and sequential model-based design with fixed or plugged-in covariance parameters
• Experimental design accounting for parameter estimation
• Towards optimization and set estimation strategies

#### Keywords

Random fields

Kriging

Positive definite kernels

Conditional simulation

Experimental Design

#### Learning Prerequisites

##### Important concepts to start the course

Linear Algebra

Basics in probability and statistics

Hilbert spaces

Notions of programming (Illustrations and computer labs in R along the semester; possible use of other languages to be discussed with the lecturer)

#### Assessment methods

Combined continuous and final assessment

The nature of the final exam (oral or written) will be decided based on the number of students.

"Dans le cas de l¿art. 3 al. 5 du Règlement de section, l¿enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés."

### In the programs

• Mathematics - master program, 2019-2020, Master semester 1
• Semester
Fall
• Exam form
During the semester
• Credits
5
• Subject examined
Spatial statistics
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics - master program, 2019-2020, Master semester 3
• Semester
Fall
• Exam form
During the semester
• Credits
5
• Subject examined
Spatial statistics
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 1
• Semester
Fall
• Exam form
During the semester
• Credits
5
• Subject examined
Spatial statistics
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 3
• Semester
Fall
• Exam form
During the semester
• Credits
5
• Subject examined
Spatial statistics
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks

MoTuWeThFr
8-9
9-10
10-11 MAA112
11-12
12-13
13-14 MAA112
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German