School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK.
Bull Math Biol. 2023 Aug 31;85(10):90. doi: 10.1007/s11538-023-01200-0.
Estimating model parameters is a crucial step in mathematical modelling and typically involves minimizing the disagreement between model predictions and experimental data. This calibration data can change throughout a study, particularly if modelling is performed simultaneously with the calibration experiments, or during an on-going public health crisis as in the case of the COVID-19 pandemic. Consequently, the optimal parameter set, or maximal likelihood estimator (MLE), is a function of the experimental data set. Here, we develop a numerical technique to predict the evolution of the MLE as a function of the experimental data. We show that, when considering perturbations from an initial data set, our approach is significantly more computationally efficient that re-fitting model parameters while producing acceptable model fits to the updated data. We use the continuation technique to develop an explicit functional relationship between fit model parameters and experimental data that can be used to measure the sensitivity of the MLE to experimental data. We then leverage this technique to select between model fits with similar information criteria, a priori determine the experimental measurements to which the MLE is most sensitive, and suggest additional experiment measurements that can resolve parameter uncertainty.
估计模型参数是数学建模的关键步骤，通常涉及最小化模型预测与实验数据之间的差异。在研究过程中，校准数据可能会发生变化，特别是如果建模是与校准实验同时进行的，或者在持续的公共卫生危机期间，如 COVID-19 大流行期间。因此，最优参数集或最大似然估计 (MLE) 是实验数据集的函数。在这里，我们开发了一种数值技术来预测 MLE 随实验数据的演变。我们表明，当考虑初始数据集的扰动时，我们的方法在重新拟合模型参数的同时，显著提高了计算效率，并且对更新的数据产生了可接受的模型拟合。我们使用连续技术来开发拟合模型参数与实验数据之间的显式函数关系，该关系可用于衡量 MLE 对实验数据的敏感性。然后，我们利用该技术在具有相似信息标准的模型拟合之间进行选择，根据先验确定 MLE 对哪些实验测量最敏感，并建议进行额外的实验测量以解决参数不确定性。
