Title: Optimal experimental design for parameter estimation in the presence of observation noise Show Chinese title

Title: 观测噪声存在时的参数估计最优实验设计

Abstract: Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is crucial; model parameters are used to both quantify observed behaviour, characterise behaviours that cannot be directly measured and make quantitative predictions. The extent to which parameter estimates are constrained by the quality and quantity of available data is known as parameter identifiability, and it is widely understood that for many dynamical models the uncertainty in parameter estimates can vary over orders of magnitude as the time points at which data are collected are varied. Here, we use both local sensitivity measures derived from the Fisher Information Matrix and global measures derived from Sobol' indices to explore how parameter uncertainty changes as the number of measurements, and their placement in time, are varied. We use these measures within an optimisation algorithm to determine the observation times that give rise to the lowest uncertainty in parameter estimates. Applying our framework to models in which the observation noise is both correlated and uncorrelated demonstrates that correlations in observation noise can significantly impact the optimal time points for observing a system, and highlights that proper consideration of observation noise should be a crucial part of the experimental design process. Show Chinese abstract

Abstract: 利用数学模型辅助解读实验在应用数学领域的研究中变得越来越重要，特别是在生物学和生态学中。 在这种背景下，准确的参数估计至关重要；模型参数不仅用于量化观察到的行为，还用于表征无法直接测量的行为，并做出定量预测。 参数估计受到可用数据质量和数量限制的程度被称为参数可辨识性，人们普遍认识到，对于许多动态模型而言，当收集数据的时间点发生变化时，参数估计的不确定性可能会以几个数量级变化。 在这里，我们使用来自Fisher信息矩阵的局部敏感性度量以及来自Sobol指数的全局度量来探讨参数不确定性如何随着测量次数及其时间分布的变化而变化。 我们将这些度量应用于优化算法，以确定导致参数估计不确定性的最低值的观测时间。 通过将我们的框架应用于观察噪声既有相关又有不相关的模型中，我们发现观察噪声的相关性可以显著影响系统观测的最佳时间点，并强调了正确考虑观察噪声应成为实验设计过程中的关键部分。