Individual-tree mortality model of Mongolian oak forests based on Bayesian method

ObjectiveThe Bayesian method is preponderant on improving the stability of model parameters. This paper explores the application of Bayesian method in the individual-tree mortality model and the improvement of estimation method of model parameters to provide reference for the growth and yield of Mongolian oak natural forests.

MethodWith the data of 202 Mongolian oak forest permanent sample plots, we developed individual-tree mortality model based on logistic model using classical method, Bayesian method and hierarchical Bayesian method. A random sample of 80% data was used for model calibration, and the remaining 20% was used for model validation. We developed individual-tree mortality model based on logistic model using classical method, Bayesian method and hierarchical Bayesian method, Bayesian statistics with prior and hierarchical Bayesian method with uninformative prior. Models were evaluated by calculating AUC (area under ROC curve) and Pearson-χ² test.

ResultThe results showed that: (1) the parameter estimated values of classical method and Bayesian method were similar, and the standard deviation of Bayesian statistics was smaller than classical method. (2) The confidence intervals of the 3 parameter estimation methods had a large coincidence. Bayesian method with informative prior had the smallest confidence interval, which was 6.0%−31.8% smaller than confidence interval of classical method. The confidence interval of hierarchical Bayesian method was more dispersed, which was 11.2%−185.0% larger than classical method. (3) The model of hierarchical Bayesian method had the best goodness of fit. The values of AUC of classical method and Bayesian method were 0.73, and the AUC value of hierarchical Bayesian method was 0.83. It is indicated that the results of the three methods are statistically significant.

ConclusionThe hierarchical Bayesian method has obvious advantages in fitting the individual-tree mortality model, whose performance is the best, and the model has the highest prediction accuracy.