A hierarchical Bayesian approach to dynamic ordinary differential equations modeling for repeated measures data on wheat growth
A hierarchical Bayesian approach to dynamic ordinary differential equations modeling for repeated measures data on wheat growth
复制标题
小麦生长重复测量数据动态常微分方程建模的分层贝叶斯方法
DOI：
10.1016/j.fcr.2022.108549
复制
发表时间：
2022
影响因子：
5.8
通讯作者：
Alderman, Phillip D.
中科院分区：
文献类型：
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作者：
Poudel, Pratishtha;Bello, Nora M.;Lollato, Romulo P.;Alderman, Phillip D.
通常使用线性混合模型分析在生长季节内收集的关于植物生长和发育的实验数据，类似于贝叶斯设置中的分层线性模型。重复测量数据的替代建模方法涉及非线性模型，如逻辑回归和基于常微分方程（ODE）系统的生态生理动态模型。然而，目前的ODE模型的实现大多是确定性的，这否定了在数据生成过程中的不确定性的认识，从而削弱了推理和预测。本研究的主要目的是演示使用动态ODE模型在贝叶斯框架内进行系统级参数的随机推断。次要目的是比较ODE模型相对于更常用于重复测量设计实验数据的方法的预测性能，即分层线性模型和分层非线性模型。使用分层贝叶斯实现，我们适合所有三种类型的模型，从冬小麦数据集的叶面积指数（LAI）和生物量的数据。在本申请的上下文中，没有一种建模方法在拟合优度或预测准确性方面明显优于任何其他方法，如由均方根误差（RMSE）、Willmott一致性指数（d）和Nash-Sutcliffe效率（NSE）的类似后验中值所指示的。ODE、线性和非线性模型的预测统计量分别为：叶面积指数的RMSEp分别为1.38、1.14和1.19; dp分别为0.91、0.93和0.93; NSEp分别为0.69、0.78和0.76;生物量的NSEp分别为0.82、0.84和0.89。动态ODE模型使生物学意义的系统级推理相关的研究问题时，不可能使用分层线性或非线性建模方法。
Experimental data collected on growth and development of plants over a growing season are typically analyzed using a linear mixed model, analogous to a hierarchical linear model in a Bayesian setting. Alternative modeling approaches for repeated measures data involve non-linear models such as logistic regression and ecophysiological dynamic models based on a system of ordinary differential equations (ODE). Yet, current implementations of ODE models are mostly deterministic in nature, which negates recognition of uncertainty in the data generation process and thus impairs inference and prediction. The primary objective of this study was to demonstrate the use of a dynamic ODE model within a Bayesian framework to make stochastic inference on system-level parameters. A secondary objective was to compare the predictive performance of an ODE model relative to methodologies more commonly used for repeated measures data from designed experiments, namely hierarchical linear models and hierarchical non-linear models. Using a hierarchical Bayesian implementation, we fit all three types of models to data on leaf area index (LAI) and biomass from a winter wheat dataset. In the context of this application, none of the modeling approaches clearly outperformed any other in terms of goodness of fit or prediction accuracy as indicated by similar posterior median values for root mean squared error (RMSE), Willmott’s agreement index (d), and Nash-Sutcliffe efficiency (NSE). The prediction statistics for the ODE, linear, and non-linear models respectively, were:RMSEpof 1.38, 1.14, and 1.19;dpof 0.91, 0.93, and 0.93; andNSEpof 0.69, 0.78, and 0.76 for LAI andRMSEpof 274.08, 253.04, and 207.63;dpof 0.95, 0.95, and 0.97; andNSEpof 0.82, 0.84, and 0.89 for biomass. The dynamic ODE model enabled biologically meaningful system-level inferences relevant to the research questions that were not possible when using the hierarchical linear or non-linear modeling approaches.