# Computer experiments & Experimental Design

## Presentation

Program (detailed content) :

Experimental Design Part :

• Linear covariance models, multiple interactions, mixed models.
• Principle of randomized experiments and classical experiments design
• Factorial, fractional designs
• Examples with the SAS or JMP software

Computer Experiment Part :

• Introduction: computer experiments and metamodelling. Examples of applications
• Two famous metamodels : chaos polynomials and Gaussian process regression (Kriging)
• Simulation of unconditional / conditional Gaussian processes
• Accounting for external knowledge and covariance kernel customization
• Metamodel-based optimisation (Bayesian optimisation)
• Design of computer experiments: focus on space-filling design
• Global sensitivity analysis: focus on ANOVA decomposition (Sobol decomposition)
• Industrial application: uncertainty quantification

Organization :

• Course, exercises, computer lab with R and JMP  softwares.

## Objectives

At the end of this module, the student will have understood and be able to explain (main concepts) :

• The main methods of experimental design
• Metamodelling for optimization / uncertainty quantification of a computer code
• At least the two main families of metamodels : chaos polynomials and Gaussian processes
• Kernel customization to account for external knowledge
• Design of computer experiments
• Global sensivity analysis

The student should be able :

Experimental Design part :

• Plan an experiment in the framework of a linear model

Computer Experiment part :

• At a theoretical level, to do computations for:
• covariance kernels and Gaussian process
• ANOVA decomposition, Sobol indices
• At a practical level, to perform the complete methodology for analyzing a computer code
• design of experiments
• metamodel construction / evaluation
• application to optimization / uncertainty quantification of a computer code

## Needed prerequisite

• Elements of statistical modelling [I4MMMS71]
• Softwares and methods of statistical exploratory data analysis [4MMSP81]
• Gaussian vectors.

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...

## Bibliography

• Azais, J.M. et Bardet, J.M. (2005)
• Le modèle linéaire par l'exemple, Dunod.
• Gaussian process for machine learning, C. E. Rasmussen and C. K. I. Williams, The MIT Press, 2006.

http://www.gaussianprocess.org/gpml/

• B. Iooss. Revue sur l'analyse de sensibilité globale de modèles numériques. Journal de la Société Française de Statistique, 152:1-23, 2011

http://journal-sfds.fr/article/view/53