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Estimating tree height-diameter models with the Bayesian method.

ABSTRACT: Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the "best" model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.

SUBMITTER: Zhang X

PROVIDER: S-EPMC3953559 | biostudies-other | 2014

REPOSITORIES: biostudies-other

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Project description:Height:diameter ratios are an important measure of stand stability. Because of the importance of height:diameter ratios for forest management, individual-tree growth models should correctly depict height:diameter ratios. In particular, (i) height:diameter ratios should not exceed that of very dense stands, (ii) height:diameter ratios should not fall below that of open-grown trees, (iii) height:diameter ratios should decrease with increasing spacing, (iv) height:diameter ratios for suppressed trees should be higher than ratios for dominant trees. We evaluated the prediction of height:diameter ratios by running four commonly used individual-tree growth models in central Europe: BWIN, Moses, Silva and Prognaus. They represent different subtypes of individual-tree growth models, namely models with and without an explicit growth potential and models that are either distance-dependent (spatial) or distance-independent (non-spatial). Note that none of these simulators predict height:diameter ratios directly. We began by building a generic simulator that contained the relevant equations for diameter increment, height increment, and crown size for each of the four simulators. The relevant measures of competition, site characteristics, and stand statistics were also coded. The advantage of this simulator was that it ensured that no additional constraint was being imposed on the growth equations, and that initial conditions were identical. We then simulated growth for a 15- and 30-year period for Austrian permanent research plots in Arnoldstein and in Litschau, which represent stands at different age-classes and densities. We also simulated growth of open-grown trees and compared the results to the literature. We found that the general pattern of height:diameter ratios was correctly predicted by all four individual-tree growth models, with height:diameter ratios above that of open-grown trees and below that of very dense stands. All models showed a decrease of height:diameter ratios with age and an increase with stand density. Also, the height:diameter ratios of dominant trees were always lower than that of mean trees. Although in some cases the observed and predicted height:diameter ratios matched well, there were cases where discrepancies between observed and predicted height:diameter ratios would be unacceptable for practical management predictions.

Project description:BackgroundGenomic variants of the disease are often discovered nowadays through population-based genome-wide association studies (GWAS). Identifying genomic variations potentially underlying a phenotype, such as hypertension, in an individual is important for designing personalized treatment; however, population-level models, such as GWAS, may not capture all the important, individualized factors well. In addition, GWAS typically requires a large sample size to detect the association of low-frequency genomic variants with sufficient power. Here, we report an individualized Bayesian inference (IBI) algorithm for estimating the genomic variants that influence complex traits, such as hypertension, at the level of an individual (e.g., a patient). By modeling at the level of the individual, IBI seeks to find genomic variants observed in the individual's genome that provide a strong explanation of the phenotype observed in this individual.ResultsWe applied the IBI algorithm to the data from the Framingham Heart Study to explore the genomic influences of hypertension. Among the top-ranking variants identified by IBI and GWAS, there is a significant number of shared variants (intersection); the unique variants identified only by IBI tend to have relatively lower minor allele frequency than those identified by GWAS. In addition, IBI discovered more individualized and diverse variants that explain hypertension patients better than GWAS. Furthermore, IBI found several well-known low-frequency variants as well as genes related to blood pressure that GWAS missed in the same cohort. Finally, IBI identified top-ranked variants that predicted hypertension better than GWAS, according to the area under the ROC curve.ConclusionsThe results support IBI as a promising approach for complementing GWAS, especially in detecting low-frequency genomic variants as well as learning personalized genomic variants of clinical traits and disease, such as the complex trait of hypertension, to help advance precision medicine.

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Estimating tree height-diameter models with the Bayesian method.

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