Design of Experiments and Advanced Statistical Modelling

The course gives a broad introduction to advanced statistical modelling tools. With the basic theory of linear regression analysis as starting point, the modelling of nonlinear (but parametric) relations between explanatory and response variables, are studied. Furthermore, generalized linear models (GLM) are introduced. In those models, a function of the expected value is modeled, rather than the expected value itself. With GLM, binary response variables (0/1), as well as response variables consisting of counts or proportions, can be handled. The course also covers generalized additive models (GAM), where the dependence between the response variable and the explanatory variables can not be described by any explicit parametric model. The GAM methodology is incorporated into GLM, which enables the modeling of many different types of response variables with complex structures for the dependence of the explanatory variables. In many industrial applications, one is interested in how a response variable is affected by changes in a number of factors. By systematically changing the factor levels, it is possible to find the optimum of the response variable, in a cost effective way. In the design of experiment part of the course, The theory of the most common tools for systematic planning of experiments and methods for the analysis of experimental results, is covered. Special emphasis is put on complete and fractional two level factorial designs. Response surface methods and their designs, and strategies for sequential design of experiments are included. Finally robust designs are introduced. As support for choosing experimental designs and analyzing data, throughout the course suitable statistical software is used. Module 1 (6 ECTS): Advanced Statistical Modelling. In this Modul linear and nonlinear regression analysis are addressed, including least square error and likelihood methods for estimating the parameters in the models. General Linear Models are introduced and methods for fitting, validating and testing in such models are discussed. Further, the fundamentals of one dimensional smoothing including splines and their use in construction of General Additive Models, are introduced. Some criteria for choosing such model parameters as well as practical aspects of analysis are discussed. Module 2 (4 ECTS) Design of Experiments. The theory of the most common tools for systematic planning of experiments and methods for the analysis of experimental results, is covered. ANOVA models are introduced as special cases of general linear models. Special emphasis is put on complete and fractional two level factorial designs. Response surface methods and their designs, and strategies for sequential design of experiments are included. Furthermore, more advanced models for the analysis of variance, with random and mixed effects are treated. Finally robust designs are introduced. Module 3 (5 ECTS) Computer labs. The Module covers implementation of the introduced statistical methods with suitable statistical software.