On Stable Parameter Estimation and Forecasting in Epidemiology by the Levenberg–Marquardt Algorithm with Broyden’s Rank-one Updates for the Jacobian Operator
On Stable Parameter Estimation and Forecasting in Epidemiology by the Levenberg–Marquardt Algorithm with Broyden’s Rank-one Updates for the Jacobian Operator
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DOI：
10.1007/s11538-019-00650-9
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发表时间：
2019-07
影响因子：
3.5
通讯作者：
A. Smirnova;Benjamin Sirb;G. Chowell
中科院分区：
文献类型：
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作者：
A. Smirnova;Benjamin Sirb;G. Chowell
用时间序列数据严格校准动态模型可能会造成障碍。通常，问题是病态的，人们必须依靠适当的正则化技术来确保稳定的参数估计，从这些参数估计中可以产生具有量化不确定性的正演投影。如果将反演过程转换为非线性微分方程组约束下的非线性最小二乘，则在迭代过程的每一步都必须对系统进行数值求解，并且不能使用相应的参数-数据映射来解析计算fr<s:1>切特导数。为了解决与不稳定性和雅可比逼近相关的挑战，我们提出了一种新的正则化Levenberg-Marquardt算法，该算法具有迭代的秩一更新，用于导数算子的计算。为了测试该方案的效率，我们使用传染病传播的数学模型和英国历史上麻疹暴发的真实发病率数据进行了数值实验。
Rigorously calibrating dynamic models with time-series data can pose roadblocks. Oftentimes, the problem is ill-posed and one has to rely on appropriate regularization techniques to ensure stable parameter estimation from which forward projections with quantified uncertainty could be generated. If the inversion procedure is cast as nonlinear least squares constrained by a system of nonlinear differential equations, then the system has to be solved numerically at every step of the iterative process and the corresponding parameter-to-data map cannot be used to evaluate the Fréchet derivative analytically. To address challenges related to both instability and Jacobian approximation, we propose a novel regularized Levenberg–Marquardt algorithm with iterative rank-one updates for computation of the derivative operator. In order to test the efficiency of this scheme, we conduct numerical experiments using a mathematical model of infectious disease transmission and real incidence data of historic measles outbreaks in the UK.