A D-Optimal Design for Estimation of Parameters of an Exponential-Linear Growth Curve of Nanostructures

We consider the problem of determining an optimal experimental design for estimation of parameters of a class of complex curves characterizing nanowire growth that is partially exponential and partially linear. Locally D-optimal designs for some of the models belonging to this class are obtained by using a geometric approach. Further, a Bayesian sequential algorithm is proposed for obtaining D-optimal designs for models with a closed-form solution, and for obtaining efficient designs in situations where theoretical results cannot be obtained. The advantages of the proposed algorithm over traditional approaches adopted in recently reported nanoexperiments are demonstrated using Monte Carlo simulations. The computer code implementing the sequential algorithm is available as supplementary materials.

本研究针对一类兼具指数与线性两段特征的纳米线生长复杂曲线的参数估计最优实验设计问题展开研究。针对该类别中的部分模型，本文通过几何方法推导得到了其局部D最优设计（D-optimal design）。此外，本文提出一种贝叶斯序贯算法，既可用于求解存在闭式解的模型的D最优设计，也可在无法获取理论结果的场景下生成高效实验设计。通过蒙特卡洛（Monte Carlo）模拟实验，验证了所提算法相较于近期纳米实验中采用的传统方法的优势。实现该序贯算法的计算机代码可作为补充材料获取。