Abstract
As an important primary producer in aquatic ecosystems, the various parameters within the mathematical models are used to describe the growth of microalgae and need to be estimated by carefully designed experiments. Non-uniform sampling has proved to generate a deliberately optimized sampling temporal schedule that can benefit parameter estimation. However, the current non-uniform sampling method depends on prior knowledge of the nominal values of the model parameters. It also largely ignores the uncertainty associated with the nominal values, thus inducing unacceptable parameter estimates. This study focuses on the uncertainty problem and describes a new sampling design that couples the traditional uniform and non-uniform sampling schedules to benefit from the merits of both methods. Based on D-optimal design, we first derive the non-uniform optimal sampling points by maximizing the determinant of the Fisher information matrix. Then the confidence interval around the non-uniform sampling points is determined by Monte Carlo simulations based on the prior knowledge of parameter distribution. Finally, we wrap the non-uniform sampling points with the uniform sampling points within the confidence interval to obtain the ultimate optimal experimental design. Scenedesmus obliquus, whose growth curve follows a four-parameter model, was used as a case study. Compared with the traditional sampling design, the simulation results show that our proposed coupled sampling schedule can partly eliminate the uncertainty in parameter estimates caused by fixed systematic errors in observations. Our coupled sampling can also retain some advantages belonging to non-uniform sampling, in exploiting information maximization and managing the cost of sampling.
Highlights
As a type of phytoplankton ubiquitous in various water bodies, microalgae— their growth—have attracted wide attention [1]
Combined with the time distribution of the sampling points obtained by D optimization, it can be inferred that the purpose of setting the first optimal sampling point at the beginning of the experiment is to determine the parameter c more accurately
The last of the four optimal sampling points is at the end of the experiment; it measures the parameter d as closely as possible: that is, it determines the upper asymptote of the growth curve
Summary
As a type of phytoplankton ubiquitous in various water bodies, microalgae— their growth—have attracted wide attention [1]. For non-uniform sampling, since it tends to lead to more accurate parameter estimates and reduces the cost of the experiment, optimal experiment design has been shown to be a powerful method in predictive microbiology [39]. When the total size of samples is greater than the number of optimized sampling times determined by the principle of optimized experimental design, repeated sampling is infeasible, it could increase the amount of information obtained in microorganism growth experiments. In order to overcome the above problems, this study proposes a new sampling schedule for choosing the optimal sampling time in microalgae growth experiments This new sampling schedule couples the traditional uniform and non-uniform samplings to leverage the advantages of both while overcoming their shortcomings. The results show that without losing the general ability of parameter estimation in various situations, the proposed method could outperform other sampling methods in some particular scenarios such as observation with fixed systematic observation error
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