Optimal Experiment Design, Ill-Posed Problems
Optimal experiment design refers to model-based methods to select experimental degrees of freedom such that the information gained from the experiment is maximized. For well-posed problems, optimal experiment design methods can focus on minimizing the variance of unknown parameters since suitable estimation methods ensure that the parameter estimates are unbiased. Ill-posed problems require the incorporation of a priori knowledge to regularize the solution which leads to stable but biased estimates. Optimal experimental design methods for ill-posed problems therefore have to incorporate the bias-variance trade-off in their objective function.
A major goal of systems biology is the construction of predictive models from the combination of experimental techniques and computational methods. Typical inverse problems that arise in model building of biological systems are, e.g., the construction...
- Banga JR, Balsa-Canto E (2008) Parameter estimation and optimal experimental design. In: Wolkenhauer O, Wellstead P, Cho KH (eds) Essays in biochemistry: systems biology, vol 45. Portland Press, London, pp 195–210Google Scholar
- Bard Y (1974) Nonlinear parameter estimation. Academic, New YorkGoogle Scholar
- Bardow A (2008) Optimal experimental design of ill-posed problems: the METER approach. Comp Chem Eng 32(1–2):115–124Google Scholar
- Box GEP, Draper NR (1959) A basis for the selection of a response-surface design. J Am Stat Assoc 54(287):622–654Google Scholar
- Draper NR, Guttman I, Lipow P (1977) All-bias designs for spline functions joined at axes. J Am Stat Assoc 72(358):424–429Google Scholar
- Engl HW, Hanke M, Neubauer A (1996) Regularization of inverse problems. Kluwer, DordrechtGoogle Scholar
- Engl HW, Flamm C, Kügler P, Lu J, Müller S, Schuster P (2009) Inverse problems in systems biology. Inverse Probl 25(12):123014Google Scholar
- Weese J (1992) A reliable and fast method for the solution of Fredholm integral-equations of the 1st kind based on Tikhonov regularization. Comput Phys Commun 69(1):99–111Google Scholar