ENBIS: European Network for Business and Industrial Statistics

The building of experimental designs from observational data

21 September 2009, 16:25 – 16:45

Abstract

Submitted by

Rossella Berni

Authors

Rossella Berni, Davide De March, Federico M. Stefanini

Affiliation

Department of Statistics – University of Florence- Viale Morgagni 59, 50134 -Florence (Italy)

Abstract

The building of experimental designs from observational data requires a deepened attention by considering the theoretical and applicative aspects.
Moreover high dimensional experimental domains make difficult to exploit classical experimental design due to the combinatorial explosion of factors and their interactions. The efficient use of these data implies the extraction of information for building an optimal experimental design through a selection of an initial set of trials.
In addition, in high dimensional data, difficulties are mainly related to the violation of fundamental principia in the experimental design: lack of randomization and efficiency.
In this paper, we consider and compare optimal experimental design criteria and Evolutionary Neural Network design from an applicative point of view.
By considering optimal design criteria, starting from previous work (Berni, 2006), a multi-step procedure in which each step aims for improving towards optimality of the selected trials, where the final set of trials constitutes an optimal experimental design built through sequential plans, is applied. Furthermore, the D and T-optimality criteria are here considered. Nevertheless, in order to improve the selection of the best final statistical model and, therefore, of the best optimal experimental design, the class of Generalized Linear Models (GLMs) could be taken into account. In fact, it is well known in the literature, the relevant contribute of this class of models to the technological field; in this paper, GLMs may improve the selection of each experimental point by evaluating the informative contribution of the selected trial by dividing between location and dispersion effects.
In comparison with the optimal design criteria, we perform a design of experiment based on Neural Network models in an evolvable approach to the data. Previous work show that a sequential evolutionary Neural Network approach performs much better under high dimensionality than the simple Genetic Algorithm. Moreover ENN has been shown to be effective in information processing of current experiments to design the next generation of experimental points (De March et al. 2008). This sequential method leads towards new experiments that are expected to have an increased amount of information about the process under study, reaching a convergence to a local/global optimal set of experiments in few generations and reducing experimental time and costs.
An empirical case study on simulated data related to a foaming process is presented.

References
Berni R., 2003b, “The use of observational data to implement an optimal experimental design”, Quality and Reliability Engineering International, Special Issue, Vol. 19 n.4, J.Wiley & Sons Ltd., West Sussex, UK, 2003, pagg.: 307-315
D. De March, M. Forlin, D. Slanzi, I. Poli (2008) Predictive Neural Networks in the design of experiments, Proceedings Wivace08, Venice, Italy

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