Understanding the Evolution of Tree Size Diversity within the Multivariate Nonsymmetrical Diffusion Process and Information Measures

Abstract

This study focuses on the stochastic differential calculus of Itô, as an effective tool for the analysis of noise in forest growth and yield modeling. Idea of modeling state (tree size) variable in terms of univariate stochastic differential equation is exposed to a multivariate stochastic differential equation. The new developed multivariate probability density function and its marginal univariate, bivariate and trivariate distributions, and conditional univariate, bivariate and trivariate probability density functions can be applied for the modeling of tree size variables and various stand attributes such as the mean diameter, height, crown base height, crown width, volume, basal area, slenderness ratio, increments, and much more. This study introduces generalized multivariate interaction information measures based on the differential entropy to capture multivariate dependencies between state variables. The present study experimentally confirms the effectiveness of using multivariate interaction information measures to reconstruct multivariate relationships of state variables using measurements obtained from a real-world data set.