Model discrimination—another perspective on model-robust designs (original) (raw)

Model-robust and model-sensitive designs

Computational Statistics & Data Analysis, 2005

The main drawback of the optimal design approach is that it assumes the statistical model is known. In this paper, a new approach to reduce the dependency on the assumed model is proposed. The approach takes into account the model uncertainty by incorporating the bias in the design criterion and the ability to test for lack-of-fit. Several new designs are derived in the paper and they are compared to the alternatives available from the literature.

Model Discrimination Criteria on Model-Robust Designs

Recently, interest about model discrimination has been focused on methods based on model estimation. Due to the problem of model aliasing, several criteria have been proposed aimed at assessing the capacity of a design for model discrimination. Three of these measures, along with a new criterion that combines them and assesses the overall discrimination capacity of a design, are implemented to evaluate a class of 27-run orthogonal arrays in three levels.

Comparing robustness properties of optimal designs under standard and compound criteria

arXiv: Methodology, 2017

Standard optimality criteria (e.g. A-, D-optimality criterion, etc.) have been commonly used for obtaining optimal designs. For a given statistical model, standard criteria assume the error variance is known at the design stage. However, in practice the error variance is estimated to make inference about the model parameters. Modified criteria are defined as a function of the standard criteria and the corresponding error degrees of freedom, which may lead to extreme optimal design. Compound criteria are defined as the function of different modified criteria and corresponding user specified weights. Standard, modified, and compound criteria based optimal designs are obtained for 333^333 factorial design. Robustness properties of the optimal designs are also compared.

Comparing robust properties of A, D, E and G-optimal designs

Computational Statistics & Data Analysis, 1994

We examine the A, D, E and G-efficiencies of using the optimal design for the polynomial regression model of degree k when the hypothesized model is of degree j and 1 Q j < k Q 8. The robustness properties of each of these optimal designs with respect to the other optimal&y criteria are also investigated. Relationships among these efficiencies are noted and practical implications of the results are discussed. In particular, our numerical results show E-optimal designs possess several properties not shared by the A, D and G-optimal designs.

Optimal design and the model validity range

Journal of Statistical Planning and Inference, 1998

A class of model-robust optimal designs, based on an extension of the standard optimality criteria to cases where there exist some prior information on the validity of a response function, is considered. Under this set-up, the concept of the "model validity range" is introduced and explored. A necessary condition for optimality is obtained for the determinant criterion (Doptimality in the classical case). A modiÿed version of this criterion is proposed and discussed. The corresponding results provide upper and low bounds for the original problem and help to construct approximate solutions, when contamination is relatively small. Optimal designs for simple but commonly used regression models are obtained and studied.

A weighted D-optimality criterion for constructing model-robust designsin the presence of block effects

2020

It is generally known that blocking can reduce unexplained variation, and in response surface designs block sizes can be pre-specified. This paper proposes a novel way of weighting D-optimality criteria obtained from all possible models to construct robust designs with blocking factors and addresses the challenge of uncertainty as to whether a first-order model, an interaction model, or a second-order model is the most appropriate choice. Weighted D-optimal designs having 2 and 3 variables with 2, 3, and 4 blocks are compared with corresponding standard D-optimal designs in terms of the D N-efficiencies. Effects of blocking schemes are also investigated. Both an exchange algorithm (EA) and a genetic algorithm (GA) are employed to generate the model-robust designs. The results show that the proposed D w-optimality criterion can be a good alternative for researchers as it can create robust designs across the set of potential models.

Robust TTT-optimal discriminating designs

The Annals of Statistics, 2013

This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the T -optimality criterion introduced by . T -optimal designs depend on unknown model parameters and it is demonstrated that these designs are sensitive with respect to misspecification. As a solution of this problem we propose a Bayesian and standardized maximin approach to construct robust and efficient discriminating designs on the basis of the Toptimality criterion. It is shown that the corresponding Bayesian and standardized maximin optimality criteria are closely related to linear optimality criteria. For the problem of discriminating between two polynomial regression models which differ in the degree by two the robust T -optimal discriminating designs can be found explicitly. The results are illustrated in several examples.

A criterion for model-robust design of experiments

Proceedings of the 2004 14th IEEE Signal Processing Society Workshop Machine Learning for Signal Processing, 2004., 2004

The paper considers the design of experiments for linear models with misspecification, of the form t(x) = Sigmai = 1 p thetasiPhii(x) + r(x), where r(x) is an unknown deviation from the regression model. Considering a modeling of this misspecification, the goal is to obtain robust designs which minimize the integral quadratic risk. A kernel-based representation (Gaussian process) is chosen