A bootstrap-based method for optimal design of experiments

作者：Paquet Durand O; Zettel V; Hitzmann B

来源：Journal of Chemometrics, 2016, 30(10): 567-574.

DOI：10.1002/cem.2820

• bootstrapping
• Cramer-Rao lower bound
• optimal design of experiments
• Peleg model
• water absorption

Bootstrapping can be used for the estimation of parameter variances, and it is straightforward to be implemented but computationally demanding compared with other methods for parameter error estimation. It is not bound to any restrictions such as the distribution of measurement errors. And because of the possible asymmetry of the probability densities of the parameters, the parameter estimation errors acquired by bootstrapping are likely to be more accurate. In this work the feasibility of a bootstrap-based method for optimal experimental design was evaluated for the Peleg model. The optimal design was performed, based on the Cramer-Rao lower bound as a benchmark. Afterwards, the optimal design was calculated based on the bootstrap method. It is demonstrated that a bootstrap-based optimal design of experiments will give comparable results with the Cramer-Rao lower bound optimal designs, however with slightly different measurement points in time. If the parameter errors obtained from both optimal experimental designs are compared, they deviate for the 2 methods on average by 1.5%. Bootstrapping can be used for problems, which cannot be solved using Cramer-Rao lower bound because of necessary but invalid assumptions. However, the benefits of the bootstrap method come at the cost of a significant increase in computational effort. Under similar conditions, the computation time for a bootstrap-based optimal design was 25minutes compared with 5seconds when using the Cramer-Rao lower bound method. As computers get faster and faster over time, the increase in computational demand will probably become less relevant in the future.
In this contribution, an optimal design of experiments for the determination of the parameters of the Peleg model has been performed. For the parameter error estimation, a bootstrap-based approach has been used and has been compared to the normal Cramer-Rao lower bound method. Although bootstrapping is computationally more demanding, it has no requirements on the distributions of the measurements or the parameter values. Therefore, it is more flexible and has the potential to be more accurate.

• 出版日期2016-10