Lecture 13: Standard algorithms for the computation of optimal designs (exact or approximate)
Optimal design of experiments
is a domain at the interface between mathematical optimization and statistics.
It studies how to optimally select experiments, when the goal
is to obtain the most accurate estimation of some unkwnown parameter.
The field of optimal experimental designs is interdisciplinary in nature,
and involes a unique mixture of linear algebra,
geometry, mathematical programming, statistics,
and graph theory.
In this course, we will review classical results from the litterature on
optimal experimental designs, with an important focus on the
underlying geometry of the problem. Covered topics will include
Introduction to linear models and applications
Linear Algebra and Geometry of confidence ellipsoids
Standard Optimality Criterions
General Equivalence theorem
Optimal Design for Polynomial Regression
Algorithms for the construction of optimal designs
Introduction to Semidefinite Programming (SDP)
Combinatorics of block designs, relation with graph theory
No prerequisite is needed. The necessary background in statistics will be reviewed within the lecture.
Wednesday 10:15-11:45. Room SR 210/A3 Seminarraum (Arnimallee 3 / 3A)
From June 4th, the lecture will start 15 minutes earlier (10:00-11:45).
First lecture is on Wednesday, 16 Apr. 2013.
Oral examination on Friday, 25.07.2014.
The material for this course is mailny based on the following references:
F. Pukelsheim, Optimal Design of Experiments.
V.V. Fedorov, Theory of optimal experiments.
S. Boyd and L. Vandenberghe, Convex Optimization.
(A free version of this book is available here.)
A.W. Marshall, I. Olkin and B.C. Arnold, Inequalities: Theory
of majorization and Its Applications (2d Edition).
As well as on the following research articles (preprints are available on the Internet):
R.A. Bailey, and P.J. Cameron, Combinatorics of optimal designs , Surveys in Combinatorics 365 (2009): 19-73.