Estimating tree height-diameter models with the Bayesian method

Area of Science:

• Forestry and Ecological Modeling
• Statistical Modeling in Ecology

Background:

• Accurate height-diameter (H-D) models are crucial for forest inventory and management.
• Traditional H-D model estimation relies on frequentist approaches like nonlinear least squares (NLS) and maximum likelihood (ML).
• Bayesian methods offer an alternative by treating parameters as random variables, potentially improving estimation.

Purpose of the Study:

• To compare the performance of classical and Bayesian methods in estimating six candidate height-diameter models.
• To evaluate the impact of informative versus uninformative priors in Bayesian estimation.
• To assess prediction accuracy and parameter estimation precision between methods.

Main Methods:

• Estimation of six height-diameter models using both classical (NLS/ML) and Bayesian approaches.
• Application of the Weibull model as the best-performing model identified from initial analysis.
• Comparison of Bayesian methods with informative and uninformative priors against the classical method using a second dataset.

Main Results:

• Both classical and Bayesian methods identified the Weibull model as the best-performing model.
• Bayesian estimation resulted in narrower confidence bands for predicted values compared to the classical method.
• Informative priors in the Bayesian approach yielded narrower credible bands for parameters than uninformative priors and the classical method.

Conclusions:

• The Bayesian method, especially with informative priors, enhances prediction accuracy and parameter estimation precision for height-diameter models.
• The Weibull model is robust across both classical and Bayesian estimation frameworks.
• Posterior distributions from Bayesian analysis can be effectively utilized as priors for subsequent estimations.