Bayesian parameter estimation of dominant height growth model for Changbai larch (Larix olgensis Henry) plantations

Bayesian inference is an alternative method of statistical inference based on prior and data information. It has become an important statistical method for forest growth modeling. With 1 687 pairs of the dominant height and age data of Changbai larch (Larix olgensis Henry) plantations, we developed dominant height-age model based on Richards equation by using classical and Bayesian methods, and discussed model reliability with small sample size and Bayesian method. To test model performance for small sample size, four sample size options were employed including all data,10%, 5% and 2% of all sample randomly selected. We examined model performance and the distribution of parameters among methods for parameter estimation covering classical statistics (nonlinear least squares method), Bayesian statistics with uninformative prior and informative prior. Models were evaluated by root mean square error (RMSE), DIC and the confidence intervals of parameters. Results showed that the results of Bayesian statistics with small sample size was very close to those of classical statistics with large sample size, while the model reliability using Bayesian method was better than classical method, and RMSE with 5% sample was the smallest. Bayesian method with informative priors has the best performance for 5% sample. Compared with non-informative priors, the fitting results by Bayesian with informative priors were better, distribution was more concentrated and it had less uncertainty. The distribution of parameters estimated from Bayesian method with informative prior was largely overlapped with that from classical method. In addition, the results of Bayesian statistics with informative priors based on three different sample sizes showed that both the standard deviations of parameters and the RMSE of model were the smallest with 5% sample. It indicated that the fitting precision of Bayesian statistics and parameters uncertainty also had a certain relationship with sample size. The study confirmed the advantages of Bayesian method in model parameter estimation of forest growth for small sample size and using informative priors.