The main objective of this course is to explore Design of Experiments with Nonlinear Models,we initially fit the student in the area of linear and nonlinear modeling, to review basic knowledge. Assumptions and methods of model linearization are addressed. Then we introduce the notion of Locally Optimal Plans by exploring Optimization criteria, illustrating the canonical form and some geometric aspects of the models. Static Plans are studied under different approaches and using the Maximin criterion. Sequential Plans and Approximate Confidence Regions are explored, concluding the UC with the experimental part, presenting several examples and their computation using the R software. The student will also be provided with contact with the analysis and validation methodologies of the estimated models, by comparison with the theoretical assumptions.
Upon completion of this learning module, the student should be able to:
1. Describe and interpret fundamental concepts of nonlinearity;
2. Perform Designs for Subsets of Parameters;
3. To approach Geometrical aspects of NLDM (Non-Linear Design Models);
4. Conduct experiments under Static Designs;
5. Perform and interpret Sequential Designs;
6. To simulate and proceed with Aproximate Confidence Regions interpretation;
7. Identify the main research and development areas on NLED;
8. Use NLDM in real practical contexts using R.
1. Introduction, notation and basic concepts.
2. Model linearization: assumptions and methods.
3. Locally Optimal Designs: canonical form and geometrical aspects.
4. Static Designs: different approaches and Maxi-min criteria.
5. Sequential Designs.
6. Approximate Confidence Regions.
7. Examples and Computation using Software R.
1. Bates, D.M., Watts, D.G.(1988). Nonlinear Regression Analysis and ItsApplications. John Wiley & Sons, Inc.
2. Fedorov, V.V., Sergei L., Leonov, S.L.(2019). Optimal Design for Nonlinear
Response Models.1st Edition. CRC Press
3. Kitsos, P. C. (2013). Optimal Experimental Design for Non-Linear Models: Theory and Applications. SpringerBriefs in Statistics. DOI 10.1007/978-3-64245287-1. Springer Heidelberg New York Dordrecht London.
Evaluation is made on individual basis and it involves the coexistence of two modes: continuous assessment (at least 60%) and final evaluation (at most 40%). Further information is detailed in the Learning Agreement of the course unit.