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Numerical aspects of uncertainty in the design of optimal experiments for model discrimination

Hoffmann, Christian

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Abstract

This thesis investigates robust strategies of optimal experimental design for discrimination between several nonlinear regression models. It develops novel theory, efficient algorithms, and implementations of such strategies, and provides a framework for assessing and comparing their practical performance. The framework is employed to perform extensive case studies. Their results demonstrate the success of the novel strategies.

The thesis contributes advances over existing theory and techniques in various fields as follows:

The thesis proposes novel “misspecification-robust” data-based approximation formulas for the covariances of maximum-likelihood estimators and of Bayesian posterior distributions of parameters in nonlinear incorrect models. The formulas adequately quantify parameter uncertainty even if the model is both nonlinear and systematically incorrect.

The thesis develops a framework of novel statistical measures and tailored efficient algorithms for the simulation-based assessment of covariance approximations for maximum-likelihood estimator for parameters. Fully parallelized variants of the algorithms are implemented in the software package DoeSim.

Using DoeSim, the misspecification-robust covariance formula for maximum-likelihood estimators (MLEs) and its “classic” alternative are compared in an extensive numerical case study. The results demonstrate the superiority of the misspecification-robust formula.

Two novel sequential design criteria for model discrimination are proposed. They take into account parameter uncertainty with the new misspecification-robust posterior covariance formula. It is shown that both design criteria constitute an improvement over a popular approximation of the Box-Hill-Hunter-criterion. In contrast to the latter, they avoid to overestimate the expected amount of information provided by an experiment.

The thesis clarifies that the popular Gauss-Newton method is generally not appropriate for finding least-squares parameter estimates in the context of model discrimination. Furthermore, it demonstrates that a large class of optimal experimental design optimization problems for model discrimination is intrinsically non-convex even under strong simplifying assumptions. Such problems are NP-hard and particularly difficult to solve numerically.

A framework is developed for the quantitative assessment and comparison of sequential optimal experimental design strategies for model discrimination. It consists of new statistical measures of their practical performance and problem-adapted algorithms to compute these measures. A state-of-the-art modular and parallelized implementation is provided in the software package DoeSim. The framework permits quantitative analyses of the broad range of behaviour that a design strategy shows under fluctuating data.

The practical performance of four established and three novel sequential design criteria for model discrimination is examined in an extensive simulation study. The study is performed with DoeSim and comprises a large number of model discrimination problems. The behaviour of the design criteria is examined under different magnitudes of measurement error and for different number of rival models.

Central results from the study are that a popular approximation of the Box-Hill-Hunter-criterion is surprisingly inefficient, particularly in problems with three or more models, that all parameter-robust design criteria in fact outperform the basic Hunter-Reiner-strategy, and that the newly proposed novel design criteria are among the most efficient ones. The latter show particularly strong advantages over their alternatives when facing demanding model discrimination problems with many rival model and large measurement errors.

Item Type: Dissertation
Supervisor: Bock, Prof. Dr. Dr. h.c. mult. Hans Georg
Date of thesis defense: 13 December 2016
Date Deposited: 28 Mar 2017 12:49
Date: 2017
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Mathematics
The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
The Faculty of Mathematics and Computer Science > Department of Computer Science
Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 004 Data processing Computer science
310 General statistics
500 Natural sciences and mathematics
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