Estimating Tree Height-Diameter Models with the Bayesian Method

Abstract

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the “best” model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.

Airborne LIDAR-Derived Aboveground Biomass Estimates Using a Hierarchical Bayesian Approach

“…Bayesian estimation is used to combine new evidence and prior distributions with the Bayesian theorem to get a new probability. Zhang et al [16,29] presented the Bayesian rules in detail. Let y = (y 1 , y 2 , y 3 , .…”

“…The best DBH and AGB model was chosen from the value of the deviance information criterion (DIC) [16], when pooling the data:…”

“…The application of LIDAR technology has reduced the cost of forest management and provided a good opportunity for large-scale forest inventory [11,12].The Bayesian method is used to integrate prior information about unknown parameters with the sample information; then, the posterior information is obtained according to the Bayes formula and the method of unknown parameters is further inferred according to the posterior information. Many studies have already used the Bayesian method to develop DBH and AGB models and have compared the Bayesian model with the classical model [14][15][16][17]. presented a comparison of aboveground biomass estimation in different sample sizes using the Bayesian method and the classical method.…”

Tree dieback affects climate change mitigation potential of a dry afromontane forest in northern Ethiopia

“…Usually, non-linear functions, including the power-law function are used to construct predictive relationships between tree H and D (Zhang et al, 2014). A power-law relationship between tree height and diameter is biologically feasible, particularly for trees with diameters <30 cm) (Muller-Landau et al, 2006;Osman et al, 2013).…”

“…Therefore, by considering our data range (see Table 1), we constructed site-specific H:D allometric equations using a power-law function (Ketterings et al, 2001;Muller-Landau et al, 2006), for living trees of J. procera and O. europaea, and a third equation by pooling all other species together. These models were used to derive H for few individuals without H measurement from their observed D (Zhang et al, 2014).…”