A multidimensional statistical model for wood data analysis, with density estimated from CT scanning data as an example

Abstract

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.