The use of copulas to practical estimation of multivariate stochastic differential equation mixed effects models

Rupšys, Petras

doi:10.1063/1.4934322

Cited by 11 publications

(11 citation statements)

References 10 publications

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“…However, all SDE taper models (1)(2)(3)(4) used additional measurements, which fixed the tree diameter at stem height h = 0. Comparison of the statistical indices produced by the regression taper models (5-8; extra integral by Equation (39)) and the regression volume models (9)(10)(11)(12) revealed that the regression volume models were superior to the regression taper models. In Models 3 and 4, the random effects calibrated by Equation (30) (using two additional stem diameter observations measured at a stem height of 1.0 m and 1.5 m for all stems in the validation data set) improved all statistical indices for the volume predictions (see Validation Data Set columns in Table 4).…”

Section: Comparison Of Stem Volume Modelsmentioning

confidence: 99%

“…All results are obtained in the Maple computer algebra system. Symmetry 2020, 12, 80 2 of 17 uses two joining points to link three stem sections along the bole, where each section is modeled by a different type of fixed-effect parameters SDE.Stochastic differential equations are widely used to model biological dynamical systems in which a stochasticity phenomenon plays a leading role, embracing more complex variations in the dynamics and generalizing classical ordinary differential equation models [10,11]. The analytical theory of univariate diffusion processes has been successfully utilized for modeling the growth dynamics of an even-age stand [12,13].…”

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Models for Tree Taper Form: The Gompertz and Vasicek Diffusion Processes Framework

2020

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In this work, we employ stochastic differential equations (SDEs) to model tree stem taper. SDE stem taper models have some theoretical advantages over the commonly employed regression-based stem taper modeling techniques, as SDE models have both simple analytic forms and a high level of accuracy. We perform fixed- and mixed-effect parameters estimation for the stem taper models by developing an approximated maximum likelihood procedure and using a data set of longitudinal measurements from 319 mountain pine trees. The symmetric Vasicek- and asymmetric Gompertz-type diffusion processes used adequately describe stem taper evolution. The proposed SDE stem taper models are compared to four regression stem taper equations and four volume equations. Overall, the best goodness-of-fit statistics are produced by the mixed-effect parameters SDEs stem taper models. All results are obtained in the Maple computer algebra system.

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Section: Comparison Of Stem Volume Modelsmentioning

confidence: 99%

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confidence: 99%

Models for Tree Taper Form: The Gompertz and Vasicek Diffusion Processes Framework

2020

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“…This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of various outcomes. There is a general tendency in the population growth modeling literature to favor flexible techniques that represent features of multivariate data as well as possible [10,11]. Therefore, multivariate SDEs describing population growth models contain both the main effects and interaction effects involved in models using a variance-covariance matrix, improving the potential to interpret the data more informatively [12] and inferring the causality in a statistical sense as a type of dependence of the multivariate random variables [13].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Models to Qualify Stem Tapers

et al. 2020

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This study examines the performance of 11 tree taper models to predict the diameter of bark at any given height and the total stem volume of eight dominant tree species in the boreal forests of Lithuania. Here, we develop eight new models using stochastic differential equations (SDEs). The symmetrical Vasicek model and asymmetrical Gompertz model are used to describe tree taper evolution, as well as geometric-type diffusion processes. These models are compared with those traditionally used for four tree taper models by using performance statistics and residual analysis. The observed dataset consists of longitudinal measurements of 3703 trees, representing the eight dominant tree species in Lithuania (pine, spruce, oak, ash, birch, black alder, white alder, and aspen). Overall, the best goodness of fit statistics of diameter predictions produced the SDE taper models. All results have been implemented in the Maple computer algebra system using the "Statistics" and "VectorCalculus" packages.

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“…Much research has been conducted on the utilization of various theoretical functions for height and diameter distribution modeling techniques for improving stand volume prediction, such as Johnson’s [4–5], beta distribution [6], and power-normal [3]. Recently, there were also a few results published on the use of the copula approach for the modeling of tree height and diameter distribution in stands [7], [8]. …”

Section: Introductionmentioning

confidence: 99%

New Insights into Tree Height Distribution Based on Mixed Effects Univariate Diffusion Processes

Rupšys

2016

PLoS ONE

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The aim of this paper is twofold: to introduce the mathematics of stochastic differential equations (SDEs) for forest dynamics modeling and to describe how such a model can be applied to aid our understanding of tree height distribution corresponding to a given diameter using the large dataset provided by the Lithuanian National Forest Inventory (LNFI). Tree height-diameter dynamics was examined with Ornstein-Uhlenbeck family mixed effects SDEs. Dynamics of a tree height, volume and their coefficients of variation, quantile regression curves of the tree height, and height-diameter ratio were demonstrated using newly developed tree height distributions for a given diameter. The parameters were estimated by considering a discrete sample of the diameter and height and by using an approximated maximum likelihood procedure. All models were evaluated using a validation dataset. The dataset provided by the LNFI (2006–2010) of Scots pine trees is used in this study to estimate parameters and validate our modeling technique. The verification indicated that the newly developed models are able to accurately capture the behavior of tree height distribution corresponding to a given diameter. All of the results were implemented in a MAPLE symbolic algebra system.

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The use of copulas to practical estimation of multivariate stochastic differential equation mixed effects models

Cited by 11 publications

References 10 publications

Models for Tree Taper Form: The Gompertz and Vasicek Diffusion Processes Framework

Models for Tree Taper Form: The Gompertz and Vasicek Diffusion Processes Framework

Stochastic Models to Qualify Stem Tapers

New Insights into Tree Height Distribution Based on Mixed Effects Univariate Diffusion Processes

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