Optimum Designs for Multi-Factor Models [Paperback]

In real applications most experimental situations are influenced by a large number of different factors. In these settings the design of an experiment leads to challenging optimization problems, even if the underlying relationship can be described by a linear model. Based on recent research, this book introduces the theory of optimum designs for complex models and develops general methods of reduction to marginal problems for large classes of models with relevant interaction structures.In real applications most experimental situations are influenced by a large number of different factors. In these settings the design of an experiment leads to challenging optimization problems, even if the underlying relationship can be described by a linear model. Based on recent research, this book introduces the theory of optimum designs for complex models and develops general methods of reduction to marginal problems for large classes of models with relevant interaction structures.I General Concepts.- 1 Foundations.- 1.1 The Linear Model.- 1.2 Designed Experiments.- 2 A Review on Optimum Design Theory.- 2.1 Optimality Criteria.- 2.2 Equivalence Theorems.- 3 Reduction Principles.- 3.1 Orthogonalization and Refinement.- 3.2 Invariance.- II Particular Classes of Multi-factor Models.- 4 Complete Product-Type Interactions.- 5 No Interactions.- 5.1 Additive Models.- 5.2 Orthogonal Designs.- 6 Partial Interactions.- 6.1 Complete M-factor Interactions.- 6.2 Invariant Designs.- 7 Some Additional Results.- Appendix on Partitioned Matrices.- References.- List of Symbols.Springer Book Archives