Bayesian analysis of semiparametric linear-circular models

In many environmental and agricultural studies, data are collected on both linear and circular random variables, with possible dependence between the variables. Classically, the analysis of such data has been carried out in a classical regression framework. We propose a Bayesian hierarchical framework to handle all forms of uncertainty arising in a linear-circular data set. One novelty of our multivariate linear-circular model is that, marginally, the circular component is assumed to be a mixture model with an unknown number of von Mises (or circular normal) distributions. We use the Dirichlet process to introduce variability in the model dimensionality, and develop a simple Gibbs sampling algorithm for simulating the mixture components. Although we illustrate our methodology on von Mises mixtures, it is widely applicable. We thus avoid complicated reversible-jump Markov chain Monte Carlo methods, which are considered ideal for analyzing mixtures of unknown number of distributions. We illustrate our methodologies with simulated and real data sets. Using pseudo-Bayes factors, we also compare different models associated with both fixed and variable numbers of von Mises distributions. Our findings suggest that models associated with varying numbers of mixture components perform at least as well as those with known numbers of mixture components. We tentatively argue that model averaging associated with variable number of mixture components improves the model’s predictive power, which compensates for the lack of knowledge of the actual number of mixture components.     

The practical use of semiparametric models in field trials

This article examines the practical use of semiparametric models in the analysis of field trials—that is, models with parameterized treatment effects and additive terms derived by a data-driven approach using a locally weighted running line smoother (loess). We discuss graphical methods to identify spatial structure in the data and model selection procedures to choose the degree of smoothing. Once the spatial part of the model has been chosen, hypotheses about the treatment effects may be tested. Semiparametric models are used to analyze two barley field trials exhibiting spatial trends. The first has a single experimental treatment and a row-column design. The second has a split-plot design, and we use a semiparametric model which accounts for the randomization at the different strata of this design. We compare the semiparametric analyses with classical analyses of variance and with alternative spatial models. We find that semiparametric models give a good insight into spatial variation in the field and can improve the precision of parameter estimates.     

Smooth additive mixed models for predicting aboveground biomass

Aboveground biomass estimation in short-rotation forestry plantations is an essential step in the development of crop management strategies as well as allowing the economic viability of the crop to be determined prior to harvesting. Hence, it is important to develop new methodologies that improve the accuracy of predictions, using only a minimum set of easily obtainable information i.e., diameter and height. Many existing models base their predictions only on diameter (mainly due to the complexity of including further covariates), or rely on complicated equations to obtain biomass predictions. However, in tree species, it is important to include height when estimating aboveground biomass because this will vary from one genotype to another. This work proposes the use of a more flexible and easy to implement model for predicting aboveground biomass (stem, branches and total) as a smooth function of height and diameter using smooth additive mixed models which preserve the additive property necessary to model the relationship within wood fractions, and allows the inclusion of random effects and interaction terms. The model is applied to the analysis of three trials carried out in Spain, where nine clones at three different sites are compared. Also, an analysis of slash pine data is carried out in order to compare with the approach proposed by Parresol (Can J For Res 31:865–878, 2001).Supplementary materials accompanying this paper appear on-line     

Empirical Bayes analysis of variance component models for microarray data

A gene-by-gene mixed model analysis is a useful statistical method for assessing significance for microarray gene differential expression. While a large amount of data on thousands of genes are collected in a microarray experiment, the sample size for each gene is usually small, which could limit the statistical power of this analysis. In this report, we introduce an empirical Bayes (EB) approach for general variance component models applied to microarray data. Within a linear mixed model framework, the restricted maximum likelihood (REML) estimates of variance components of each gene are adjusted by integrating information on variance components estimated from all genes. The approach starts with a series of single-gene analyses. The estimated variance components from each gene are transformed to the “ANOVA components”. This transformation makes it possible to independently estimate the marginal distribution of each “ANOVA component.” The modes of the posterior distributions are estimated and inversely transformed to compute the posterior estimates of the variance components. The EB statistic is constructed by replacing the REML variance estimates with the EB variance estimates in the usual t statistic. The EB approach is illustrated with a real data example which compares the effects of five different genotypes of male flies on post-mating gene expression in female flies. In a simulation study, the ROC curves are applied to compare the EB statistic and two other statistics. The EB statistic was found to be the most powerful of the three. Though the null distribution of the EB statistic is unknown, a t distribution may be used to provide conservative control of the false positive rate.     

Freundlich和Temkin等温线模型热力学参数的计算

Derivation of the Freundlich and Temkin isotherm models from the kinetic adsorption/desorption equations was carried out to calculate their thermodynamic equilibrium constants.The calculation formulase of three thermodynamic parameters,the standard molar Gibbs free energy change,the standard molar enthalpy change and the standard molar entropy change,of isothermal adsorption processes for Freundlich and Temkin isotherm models were deduced according to the relationship between the thermodynamic equilibrium constants and the temperature.     

A blended estimator for a measure of agreement with a gold standard

St. Laurent developed a measure of agreement for method comparison studies in which an approximate method of measurement was compared to a gold standard method of measurement. The measure of agreement proposed was shown to be related to a population intraclass correlation coefficient. In this paper, the authors develop a family of estimators for the measure of agreement based on pivotal quantities. A blend of two particular members of the family is suggested as an estimator itself. In general, the blended estimator outperforms the maximum likelihood estimator in terms of bias and mean-squared error.     

Sensitivity analysis of soil hydrologic parameters for two crop growth simulation models

Soil characteristics are some of the most important inputs in crop simulation models like CERES-Maize and MACROS models under field conditions. A sensitivity analysis of these models was carried out for 1995 and 1996 by incorporating changes (+2, +4, +6, −2, −4, and −6%) of the measured values of three basic soil input parameters: wilting point (WP), saturated soil water content (FS) and field capacity (FC). For this purpose, eight soil profile layers were chosen for CERES-Maize and three for the MACROS model. The MACROS model was found to have a higher degree of sensitivity to changes in the relevant soil parameters than the CERES-Maize model, especially for WP. For the MACROS model, an earlier end of the growing period (75 days) for maize at the +6% level for WP was simulated in 1995 as against 152 days for the CERES-Maize model. The yield in 1995 due to 6% increase in WP resulted in a decrease of about 35% yield when CERES-Maize model was used. In 1996 the increase in WP by 6% resulted in decrease of yield by 22.5 and by 0.9% for MACROS and CERES-Maize models, respectively. When WP was decreased by 6% then the yield was found to increase by about 20.4 and 12.0% for MACROS and CERES-Maize models, respectively in 1995. In 1996 the same alteration of WP caused the yield to increase by about 5.7 and 0.7% for MACROS and CERES-Maize models. Alteration of the model's remaining parameters showed a negligible influence on yields for both the models.     

Sensitivity analysis of critical parameters in microbial maintenance-energy models

Summary Overestimates of microbial biomass and high maintenance rates have caused calculations of annual maintenance requirements to exceed annual C inputs to soil ecosystems. An integrated approach is needed to resolve this inconsistency in the literature. In the present study a mechanistic model for soil microbial systems was used to calculate the maintenance-energy requirements of the soil microbial biomass. This model is base on product formation rather than substrate use and describes an active and sustaining population, with cryptic growth and necromass recycling. Several assumptions, such as death rates, the percentage of active population, and the yield, are required to calculate the maintenance energies, and the sensitivity of these estimated parameters on the maintenance-rate calculation was tested. The total biomass and the yield factor had the greatest effect on the calculated maintenance value. The fraction of active organisms, the death rates, and the different maintenance values for each population had little effect on the maintenance value.     

基于田块尺度含水率观测的土壤水力参数多模型反演

该文利用反演工具UCODE与4种Richards方程数值模型(Ross模型、Picard-θ模型、Picard-mix模型和Picard-h模型)进行耦合,构建了4种不同的反演模型。基于田块尺度含水率观测数据,分别用4种反演模型优化了研究田块的土壤参数。研究结果表明,4种模型的反演精度依次为:Ross模型、Picard-θ模型、Picard-mix模型和Picard-h模型,但差异并不显著,反演效率以Ross模型最优。随着网格的加密,各种模型所反演参数的模拟精度改善不明显。本文还讨论了土壤水运动中"异参同效性"现象,并提出"参数曲线带"的概念——即由反求的同效参数土壤水分曲线和水力传导度曲线形成的包络图。随着模拟精度要求越高,同效参数越少,"参数曲线带"越窄,并认为反求的同效参数曲线在含水率观测信息较多的地方交汇。     

Identification of parameters in transient water quality models from stochastic data

An approach is presented for the identification of parameters in time-varying water quality models from stochastic data measured at two points along a stream (input-output type data). The models are plug flow models described by linear-first order partial differential equations. The method employed is to reduce the partial differential equations to a set of ordinary differential equations with the method of characteristics from which an analytical solution is obtained. The time-lag phenomenon presented in plug flow models is used to correlate the input-output data. A gradient method (Bard's method) is employed to identify the parameters in the correlation equation.     

基于3CCD摄像机的水稻农学参数估算

水稻农学参数的估算是调控水稻生长、预测水稻产量的重要基础和根据。该文以广东省农业科学研究院大丰农场水稻研究所的稻田为研究对象,根据植物反射光谱的特性,研究3CCD摄像机水稻叶面积指数、生物量、叶绿素含量、叶长、叶宽、株高、产量等农学参数的估算,结果表明:分蘖期农学参数不适于用3CCD摄像机估算;叶面积指数在分化期估算最准确;生物量、叶绿素含量、产量均在抽穗期估算较好;3CCD摄像机不适用于大面积水稻株高、剑叶长、剑叶宽等外部特征的估算。该文为CCD摄像机的水稻估产打下基础。     

An extension of the Lin-Yip estimator for continuous-time capture studies

A unified approach is suggested to estimate the population size for continuous time capture studies with possible removals during the capture process. It extends and improves the Lin-Yip estimator. The usual recaptureand removal models can be shown to be particular cases of the general formulation. A Horvitz-Thompson procedure is used to estimate the population size based on the estimated capture probabilities. The resultant estimators for the regression parameters and population size are consistent and asymptotically normal underappropriateregularity conditions. We assess the properties of the proposed estimators through Monte Carlo simulation. Two examples are given.     

Using SAEM to estimate parameters of models of response to applied fertilizer

Many nonlinear functions have been used to predict crop yield response to applied fertilizer. Accurate estimates of the parameter values are required for the formulation of satisfactory fertilizer dose recommendations. In fertilizer trials, several yield measurements for different fertilizer doses are usually made at the same site and in the same year. Model errors are therefore unlikely to be independent for the same site-year. Nonlinear mixed effects models can be used for yield response data. We evaluated the performance of a recently proposed stochastic approximation of the EM algorithm (SAEM) for estimating the parameters of nonlinear mixed effects models. We used the SAEM method to estimate the parameters of four different nonlinear models, using a real dataset including 37 site-years of yield measurements. We then carried out simulations, to determine the bias and the root mean squared errors of the estimators. We compared the results obtained with SAEM with those obtained using a first-order conditional method. SAEM gave better results in most cases. The estimates produced by SAEM were less biased and less affected by initial values.     

A critique of models for freshwater and soil acidification

Four types of models quantifying effects of acid deposition on freshwaters are reviewed. These include Henriksen's empirical model, an adsorption isotherm model, soil-oriented charge balance models (Reuss-Johnson, Birkenes, MAGIC, ILWAS), and the Trickle Down model. Emphasis is on an assessment of critical assumptions; no attempt has been made to run the various models and compare results. The models range from simple to very complex and from empirical to highly process oriented. The various types have all proven useful and there has been a significant convergence concerning key processes. The importance of anion mobility, sulfate adsorption, ion exchange, dissolution of Al bearing minerals and weathering seems to be accepted by most workers. Future model improvement, however, relies to a large extent on further checking against observations.     

Empirical binomial sampling plans: model calibration and testing using Williams’ method III for generalized linear models with overdispersion

Binomial sampling plans that use presence/absence data for estimating pest population density are commonly used in cropprotection when counting individual pest units is not cost effective. These plans are often based on the empirical relationship between the proportion of presences, p, and a count-based estimate of the mean population density, [(m)\tilde]\tilde \mu , given by ln{ - ln(1 - p) } = a₀ + a₁ ln([(m)\tilde] )\ln \left\{ { - \ln (1 - p)} \right\} = \alpha _0 + \alpha _1 ln(\tilde \mu ), which is typically fitted as a simple linear regression. However, correctly incorporating all of (i) binomial sampling errors, (ii) biological errors (i.e., overdispersion), and (iii) errors in variables is not possible using linear regression. Here, model calibration and testing is carried out using William’s method III for fitting a binomial generalized linear model with overdispersion (GLMw) in order to handle (i) and (ii), and simulation is used to study the effect of using the sample estimate of μ as the predictor variable. Calculation of the operating characteristics function of the decision rule for an action threshold of p ₀ is compared for linear and GLM_w models, with the former shown to substantially underestimate the probability of correct decisions and overestimate the probability of incorrect decisions. A binomial sampling plan for populations of the leaf beetle Chrysophtharta bimaculata, a defoliator of Eucalyptusnitens plantations, is used to demonstrate the methods.     

高光谱土壤多元信息提取模型综述

高光谱土壤多元信息提取模型的精度与光谱学在这一领域未来能够发挥的作用直接相关。在列举土壤样品制备、理化成分测定和土壤光谱数据获取标准技术的基础上,总结了目前适用于土壤光谱处理的异常筛选、平滑去噪、重采样、变换和定量化方法。对偏最小二乘法、主成分分析和多元逐步回归法等8种建模方法进行了对比,分析了各类方法的建模针对性。按照有机质、水分、盐渍化、重金属和其它成分分类归纳了目前取得良好应用效果的多种光谱信息提取模型,并对比了每个模型的信息提取精度。光谱所指示的信息,不仅能够为土壤成分提供快速指示信息,而且在实测数据基础上所建立的信息提取模型,是软件研发、仪器研发和土质评价等工作的理论基础。