A powerful investigative tool in biology is to consider not a single mathematical model but a collection of models designed to explore different working hypotheses and select the best model in that collection.In these...A powerful investigative tool in biology is to consider not a single mathematical model but a collection of models designed to explore different working hypotheses and select the best model in that collection.In these lecture notes,the usual workflow of the use of mathematical models to investigate a biological problem is described and the use of a collection of model is motivated.Models depend on parameters that must be estimated using observations;and when a collection of models is considered,the best model has then to be identified based on available observations.Hence,model calibration and selection,which are intrinsically linked,are essential steps of the workflow.Here,some procedures for model calibration and a criterion,the Akaike Information Criterion,of model selection based on experimental data are described.Rough derivation,practical technique of computation and use of this criterion are detailed.展开更多
冬小麦叶面积指数(leaf area index,LAI)是描述冠层结构的重要参数之一,对评价其长势和预测产量具有重要意义。该文利用灰色关联分析(grey relational analysis,GRA)对植被指数进行排序,用偏最小二乘法(partial least squares regressio...冬小麦叶面积指数(leaf area index,LAI)是描述冠层结构的重要参数之一,对评价其长势和预测产量具有重要意义。该文利用灰色关联分析(grey relational analysis,GRA)对植被指数进行排序,用偏最小二乘法(partial least squares regression,PLS)选择不同的植被指数个数作为自变量进行回归建模,通过赤池信息量准则(Akaike’s information criterion,AIC)选择AIC值最小的模型作为冬小麦LAI最优估算模型,即GRA、PLS和AIC 3种方法整合建立冬小麦LAI最优估算模型。使用2008-2009年在中国北京通州区和顺义区获取的整个生育期冬小麦LAI和配套的光谱数据进行建模,利用2009-2010相关数据进行验证。研究表明:采用GRA评价标准与冬小麦LAI关联度最大的植被指数是VOG1,关联度最小的植被指数是SR;通过AIC建立的以8个植被指数作为自变量的冬小麦LAI模型效果最优,建模集的决定系数R2和标准误SE分别为0.76和0.009,验证集的R2和相对均方根误差RRMSE分别为0.63和0.004,预测模型和验证模型均具有较高的精度和可靠性。结果表明采用GRA-PLS-AIC方法进行冬小麦LAI反演是可行的,为提高冬小麦LAI遥感预测精度提供了一种有效的方法。展开更多
基金SP is supported by a Discovery Grant of the Natural Sciences and Engineering Research Council of Canada(RGOIN-2018-04967).
文摘A powerful investigative tool in biology is to consider not a single mathematical model but a collection of models designed to explore different working hypotheses and select the best model in that collection.In these lecture notes,the usual workflow of the use of mathematical models to investigate a biological problem is described and the use of a collection of model is motivated.Models depend on parameters that must be estimated using observations;and when a collection of models is considered,the best model has then to be identified based on available observations.Hence,model calibration and selection,which are intrinsically linked,are essential steps of the workflow.Here,some procedures for model calibration and a criterion,the Akaike Information Criterion,of model selection based on experimental data are described.Rough derivation,practical technique of computation and use of this criterion are detailed.
文摘冬小麦叶面积指数(leaf area index,LAI)是描述冠层结构的重要参数之一,对评价其长势和预测产量具有重要意义。该文利用灰色关联分析(grey relational analysis,GRA)对植被指数进行排序,用偏最小二乘法(partial least squares regression,PLS)选择不同的植被指数个数作为自变量进行回归建模,通过赤池信息量准则(Akaike’s information criterion,AIC)选择AIC值最小的模型作为冬小麦LAI最优估算模型,即GRA、PLS和AIC 3种方法整合建立冬小麦LAI最优估算模型。使用2008-2009年在中国北京通州区和顺义区获取的整个生育期冬小麦LAI和配套的光谱数据进行建模,利用2009-2010相关数据进行验证。研究表明:采用GRA评价标准与冬小麦LAI关联度最大的植被指数是VOG1,关联度最小的植被指数是SR;通过AIC建立的以8个植被指数作为自变量的冬小麦LAI模型效果最优,建模集的决定系数R2和标准误SE分别为0.76和0.009,验证集的R2和相对均方根误差RRMSE分别为0.63和0.004,预测模型和验证模型均具有较高的精度和可靠性。结果表明采用GRA-PLS-AIC方法进行冬小麦LAI反演是可行的,为提高冬小麦LAI遥感预测精度提供了一种有效的方法。
