Prior distribution of parameters in each component biomass equation of published literature.

<p>Prior distribution of parameters in each component biomass equation of published literature.</p

Prior distributions of each parameter in M1-M3.

<p>Prior distributions of each parameter in M1-M3.</p

Parameter estimates of self-thinning line relationships using hierarchical Bayesian method.

<p>Parameter estimates of self-thinning line relationships using hierarchical Bayesian method.</p

Evaluation statistics of Bayesian method, and MLS method for biomass model.

<p>Evaluation statistics of Bayesian method, and MLS method for biomass model.</p

Geographical location of Chinese fir compiled in the published literature.

<p>The big blue dot is the location for the study site. Other black dots are the locations of published literature for studying Chinese fir biomass.</p

Hierarchical Bayesian estimates for the parameters in M2.

<p>Hierarchical Bayesian estimates for the parameters in M2.</p

A Hierarchical Bayesian Model to Predict Self-Thinning Line for Chinese Fir in Southern China

<div><p>Self-thinning is a dynamic equilibrium between forest growth and mortality at full site occupancy. Parameters of the self-thinning lines are often confounded by differences across various stand and site conditions. For overcoming the problem of hierarchical and repeated measures, we used hierarchical Bayesian method to estimate the self-thinning line. The results showed that the self-thinning line for Chinese fir (<i>Cunninghamia lanceolata</i> (Lamb.)Hook.) plantations was not sensitive to the initial planting density. The uncertainty of model predictions was mostly due to within-subject variability. The simulation precision of hierarchical Bayesian method was better than that of stochastic frontier function (SFF). Hierarchical Bayesian method provided a reasonable explanation of the impact of other variables (site quality, soil type, aspect, etc.) on self-thinning line, which gave us the posterior distribution of parameters of self-thinning line. The research of self-thinning relationship could be benefit from the use of hierarchical Bayesian method.</p></div

Sample trees of Chinese fir plantation with different ages.

<p>Note: Std = standard deviation.</p

Descriptive statistics of stand variables of Chinese fir stands.

<p>(<i>n</i> = 10 plots).</p

Tree Biomass Estimation of Chinese fir (<i>Cunninghamia lanceolata</i>) Based on Bayesian Method

<div><p>Chinese fir (<i>Cunninghamia lanceolata</i> (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass.</p></div