Rainer Schwabe

Digital image analysis for diagnosis of cutaneous melanoma. Development of a highly effective computer algorithm based on analysis of 837 melanocytic lesions.

Background  Digital image analysis has been introduced into the diagnosis of skin lesions based on dermoscopic pictures.

Optimum designs for multi-factor models

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.

Advances in optimum experimental design for conjoint analysis and discrete choice models

The authors review current developments in experimental design for conjoint analysis and discrete choice models emphasizing the issue of design efficiency. Drawing on recently developed optimal paired comparison designs, theoretical as well as empirical evidence is provided that established design strategies can be improved with respect to design efficiency.

Optimal paired comparison designs for first-order interactions

In many fields of applications paired comparisons are used in which either full or partial profiles of the alternatives are presented. For this situation we introduce an appropriate model and derive optimal designs in the presence of interactions when all attributes have the same number of levels.

Optimal design for the Bradley–Terry paired comparison model

Paired comparisons are a popular tool for questionnaires in psychological marketing research. The quality of the statistical analysis of the responses heavily depends on the design, i.e. the choice of the alternatives in the comparisons. In this paper we show that the structure of locally optimal designs changes substantially with the parameters in the underlying utility. This fact is illustrated by elementary examples, where the optimal designs can be completely characterized. As an alternative maximin efficient designs are proposed which perform well for all parameter settings.

Lattices and dual lattices in optimal experimental design for Fourier models

Number-theoretic lattices, used in integration theory, are studied from the viewpoint of the design and analysis of experiments. For certain Fourier regression models lattices are optimal as experimental designs because they produce orthogonal information matrices. When the Fourier model is restricted, that is a special subset of the full factorial (cross-spectral) model is used, there is a difficult inversion problem to find generators for an optimal design for the given model. Asymptotic results are derived for certain models as the dimension of the space goes to infinity. These can be thought of as a complexity theory connecting designs and models or as special type of Nyquist sampling theory.

A NOTE ON OPTIMAL BOUNDED DESIGNS

An equivalence theorem is formulated to characterize optimal designs with general prespecified direct constraints on the design intensity. As an application locally optimal designs are obtained with bounded intensity for the logistic regression model. Moreover, it is shown that, for additive models, optimal marginally bounded designs can be generated from their optimal counterparts in the corresponding marginal models.

D-optimal designs of experiments with non-interacting factors

Abstract In this paper a general result is presented on the D-optimality of product designs for experiments with non-interacting factors. In particular, D-optimal designs can be constructed as a product of those designs which are D-optimal in the corresponding single-factor models. Results are obtained for the whole parameter vector and for the parameters associated with single factors.

On a stochastic approximation procedure based on averaging

Based on the idea of averaging a new stochastic approximation algorithm has been proposed by Bather (1989), which shows a preferable performance for small to moderate sample sizes. In the present paper an almost sure representation is established for this procedure, which gives the optimal rate of convergence with minimal asymptotic variance.

Strong representation of an adaptive stochastic approximation procedure

We consider a rather general one-dimensional stochastic approximation algorithm where the steplengths might be random. Without assuming a martingale property of the random noise we obtain a strong representation by weighted averages of the error terms. We are able to apply the representation to an adaptive process in the case where the random noise is a martingale difference sequence as well as in the case where the random noise is weakly dependent and some moment conditions are statisfied.