Individual Tree Growth Model For Mongolia Oak Forest With Bayesian Statistical Inference

Bayesian inference is an alternative method of statistical inference based on data and prior information. It has been becoming an important statistical method for forest growth modeling.Based on 202 re-measured permanent sample plots of Mongolian oak forest in Wangqing Forest Bureau of Jinlin province, we developed growth model system of Mongolian oak natural uneven-aged forest.The system includes individual diameter growth model, individiual height-diameter model, individual mortality model and stand recruitment model, whose parameters were estimated by classical statistics, Bayesian and hierarchical Bayesian method.Model reliability and performance with different methods were compared and analyzed. We also tested the performance of recruitment model with small sample size. The main conclusions are as follows:(1) Model calibration showed that the mean parameters estimated by classical statistical method were very close to those of Bayesian statistics with informative priors, while the mean parameters estimated by classical method with random effects differed greatly from those of hierarchical Bayesian method.(2) The distribution of parameters estimated from Bayesian method with informative prior was largely overlapped with that from classical method, but more concentrated than the latter.While the distribution of parameters estimated from hierarchical Bayesian was greatly different from the above two methods, and the interval was the largest.(3) The mean parameters estimated by Bayesian method with informative prior were most stable, while those of hierarchical Bayesian were most unstable. Among the four models, the standard deviation of parameters estiomated by Bayesian method with informative prior were6.00%~53.00% smaller than those of classical method. And those of hierarchical Bayesian were 28%~42% smaller than calssical method with random effects.(4) The hierarchical Bayesian method had the best fitting and forecasting effect. The fitting effect(R2) with diameter growth model and tree height curve model by hierarchicalBayesian statistical increased by 36.89% and 11.60% than Maximum Likelihood respectively.And the fitting effect(AIC and DIC) of mortality model by hierarchical Bayesian statistical increased by 8.59%, the fitting effect of recruitment model with hierarchical Bayesian increased by 95.11%.(5) The hierarchical Bayesian had the highest model precision.The fitting precision of diameter growth model and tree height curve model(RMSE) by hierarchical Bayesia were17.02% and 46.99% higher than the Maximum Likelihood,respectively. The fitting precision of mortality model(AUC) by hierarchical Bayesian inreased by 12.40% and the recruitment model inreased by 98%(RMSE).(6) The hierarachical Bayesian had better performance for data with small sample size.The distribution of |ME|、RMSE and AIC(DIC) of recruitment model by hierarchical Bayesian with small sample size were smaller than the results of classical and Bayesian method with large sample size. And these error statistics were stable with the increase of sample size. With the increase of sample size, the distribution of RME and RRMSE were more concentrated.And the error statistics of Bayesian was close to classical.