THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation

Adaptive sparse polynomial chaos expansion based on least angle regression

An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis

Sensitivity analysis: A review of recent advances

Efficient computation of global sensitivity indices using sparse polynomial chaos expansions

Cette these s'insere dans le contexte generale de la propagation d'incertitudes et de l'analyse de sensibilite de modeles de simulation numerique, en vue d'applications industrielles. Son objectif est d'effectuer de telles etudes en minimisant le nombre d'evaluations du modele, potentiellement couteuses. Le present travail repose sur une approximation de la reponse du modele sur la base du chaos polynomial (CP), qui permet de realiser des post-traitements a un cout de calcul negligeable. Toutefois, l'ajustement du CP peut necessiter un nombre consequent d'appels au modele si ce dernier depend d'un nombre eleve de parametres (e. G. Superieur a 10). Pour contourner ce probleme, on propose deux algorithmes pour ne selectionner qu'un faible nombre de termes importants dans la representation par CP, a savoir une procedure de regression pas-a-pas et une procedure basee sur la methode de Least Angle Regression (LAR). Le faible nombre de coefficients associes aux CP creux obtenus peuvent ainsi etre determines a partir d'un nombre reduit d'evaluations du modele. Les methodes sont validees sur des cas-tests academiques de mecanique, puis appliquees sur le cas industriel de l'analyse d'integrite d'une cuve de reacteur a eau pressurisee. Les resultats obtenus confirment l'efficacite des methodes proposees pour traiter les problemes de propagation d'incertitudes et d'analyse de sensibilite en grande dimension

Géraud Blatman

Papers

Adaptive sparse polynomial chaos expansion based on least angle regression

An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis

Efficient computation of global sensitivity indices using sparse polynomial chaos expansions

Adaptive sparse polynomial chaos expansions for uncertainty propagation and sensitivity analysis

Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach