Model-based design of experiments for parameter precision: State of the art

Qualitative and quantitative experiment design for phenomenological models—a survey

Response surface experimentation1

Introduction.- Asymptotic designs and uniform convergence. Asymptotic properties of the LS estimator.- Asymptotic properties of M, ML and maximum a posteriori estimators.- Local optimality criteria based on asymptotic normality.- Criteria based on the small-sample precision of the LS estimator.- Identifiability, estimability and extended optimality criteria.- Nonlocal optimum design.- Algorithms-a survey.- Subdifferentials and subgradients.- Computation of derivatives through sensitivity functions.- Proofs.- Symbols and notation.- List of labeled assumptions.- References.

Design of Experiments in Nonlinear Models: Asymptotic Normality, Optimality Criteria and Small-Sample Properties

Mixture models based on homogeneous polynomials

Designs for quadratic regression are considered when the possible values of the controlable variable are mixtures x = (x 1, x 2, …, x q + 1) of nonnegative components x i with Σ q + 1 1 x i = 1. The designs that are optimum with respect to the D-, A-, and E-optimality criteria are compared in their performance relative to these and other criteria. Computational routines for obtaining these designs are developed, and the geometry of optimum structures is discussed. Except when q = 2, the A-optimum design is supported by the vertices and midpoints of edges of the simplex, as is the case for the previously known D-optimum design. Although the E-optimum design requires more observation points, it is more robust in its efficiency, under variation of criterion: but all three designs perform reasonably well in this sense.

J. Kiefer

Papers

Comparison of Simplex Designs for Quadratic Mixture Models