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首页> 外文期刊>Canadian Journal of Forest Research >A multidimensional statistical model for wood data analysis, with density estimated from CT scanning data as an example.
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A multidimensional statistical model for wood data analysis, with density estimated from CT scanning data as an example.

机译：用于木材数据分析的多维统计模型，以从CT扫描数据估算的密度为例。

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摘要

The trunk of a tree can be seen as a spatiotemporal sampling domain from the statistical perspective, where space is represented by direction horizontally and height vertically, and time through annual growth rings. In this framework, wood properties such as density can be the object of data collection for given estimation and testing purposes. We present a multidimensional statistical model, the tensor normal distribution, in which the variation (variance) of and dependency (covariance) between wood property measurements made for different years at various locations in a tree trunk can be inferred. Its application requires a smaller number of replicates (trees) than the traditional vector normal distribution because variances and covariances for directions and growth rings, for example, must be the same at all heights, up to a multiplicative constant. This assumption on the variance-covariance structure is called "separability", and we explain how to test it. An illustration with wood density estimates obtained from computed tomography scanning data for 11 white spruce (Picea glauca (Moench) Voss) trees is presented. This example is completed by assessing differences in mean wood density according to location in the trunk, with analysis-of-variance F-tests adjusted for the estimated variances and covariances obtained by fitting the model.
机译：从统计角度来看，树的树干可以看作是时空采样域，其中空间由水平方向和垂直高度以及通过年轮的时间表示。在此框架中，对于给定的估计和测试目的，木材属性（例如密度）可以作为数据收集的对象。我们提出了一个多维统计模型，即张量正态分布，其中可以推断出在树干中各个位置不同年份进行的木材性能测量之间的变化（方差）和依赖性（协方差）。它的应用需要的复制（树）数量比传统的矢量正态分布要少，这是因为例如方向和生长环的方差和协方差在所有高度上都必须相同，直到乘法常数。关于方差-协方差结构的这种假设称为“可分离性”，我们解释了如何对其进行检验。给出了从计算机断层扫描数据中获得的11棵白云杉（Picea glauca （Moench）Voss）树的木材密度估计值的示意图。通过根据树干中的位置评估平均木材密度的差异来完成此示例，并针对通过拟合模型获得的估计方差和协方差调整方差分析 F 测试。

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