Bayesian Methods for Hierarchical Distance Sampling Models

The few distance sampling studies that use Bayesian methods typically consider only line transect sampling with a half-normal detection function. We present a Bayesian approach to analyse distance sampling data applicable to line and point transects, exact and interval distance data and any detection function possibly including covariates affecting detection probabilities. We use an integrated likelihood which combines the detection and density models. For the latter, densities are related to covariates in a log-linear mixed effect Poisson model which accommodates correlated counts. We use a Metropolis-Hastings algorithm for updating parameters and a reversible jump algorithm to include model selection for both the detection function and density models. The approach is applied to a large-scale experimental design study of northern bobwhite coveys where the interest was to assess the effect of establishing herbaceous buffers around agricultural fields in several states in the US on bird densities. Results were compared with those from an existing maximum likelihood approach that analyses the detection and density models in two stages. Both methods revealed an increase of covey densities on buffered fields. Our approach gave estimates with higher precision even though it does not condition on a known detection function for the density model.     

Model‐based analysis using REML for inference from systematically sampled data on soil

The general linear model encompasses statistical methods such as regression and analysis of variance (anova ) which are commonly used by soil scientists. The standard ordinary least squares (OLS) method for estimating the parameters of the general linear model is a design‐based method that requires that the data have been collected according to an appropriate randomized sample design. Soil data are often obtained by systematic sampling on transects or grids, so OLS methods are not appropriate. Parameters of the general linear model can be estimated from systematically sampled data by model‐based methods. Parameters of a model of the covariance structure of the error are estimated, then used to estimate the remaining parameters of the model with known variance. Residual maximum likelihood (REML) is the best way to estimate the variance parameters since it is unbiased. We present the REML solution to this problem. We then demonstrate how REML can be used to estimate parameters for regression and anova ‐type models using data from two systematic surveys of soil. We compare an efficient, gradient‐based implementation of REML (ASReml) with an implementation that uses simulated annealing. In general the results were very similar; where they differed the error covariance model had a spherical variogram function which can have local optima in its likelihood function. The simulated annealing results were better than the gradient method in this case because simulated annealing is good at escaping local optima.     

The simulation of phenological development in dynamic crop model: The Bayesian comparison of different methods

The main objective of our study was to use Bayesian methods to quantify the uncertainties related to phenological development of maize (Zea mays L.) under various climate conditions. For this purpose, five different phenological methods were implemented in the dynamic crop growth model, which was subsequently optimized, using the data acquired at three different locations in Slovenia. The sensitivity analysis of the crop model was performed in order to find the set of most influential physiological parameters. Subsequent Bayesian model comparison was used in order to quantify the impact of phenological method selection on the final maize yield. The results revealed the importance of using an appropriate phenological method in order to correctly estimate the duration of the growing season and yield, when used within dynamic crop model. The limitations of the phenological methods used in this study are discussed. The selection of phenological method itself did not have a significant influence on the yield estimation, except in years with high temperatures and limiting water conditions. This raises the concern that inaccurate simulation of phenological development may increase the uncertainties of impact assessment on crop yield where crop models are fed with future climate projections.     

Making sequential analysis of environmental monitoring data feasible by simplifying the covariance matrix structure

As environmental monitoring data are collected successively in time, the data are suitable for sequential analysis. An earlier article proposed a refined sequential probability ratio test (SPRT) to test against a minimal relevanttrend, assuming no serial correlations and without modeling the spatial covariance matrix. As the model parameters are unknown in advance, a minimal number of observations(n _min) is required for estimation prior to analysis. Leaving the spatial covariance matrix unstructured, n _min increases if the number of sampling locations increases. Therefore, assumptions on the spatial covariance matrix are proposed, thereby reducing the number of nuisance parameters, thus reducingn _min. This article studies. three simple types of spatial covariance matrix structures and derives an adjusted SPRT for each of these types. Furthermore, we examine the robustness against deviations from the assumed spatial covariance matrix structure. Simulation studies show that adjusted SPRTs can be derived rather easily and that they are in general robust against deviations from the assumed type of spatial covariance matrix. Sequential analysis of simulated data, which are based on monitoring data of bats in the Netherlands, illustrates the use of one of the derived SPRTs.     

基于无人机图像纹理和表型参数的夏玉米水分胁迫诊断

农田水分胁迫是影响作物生长发育和产量品质的重要原因。及时准确地诊断作物水分胁迫状况,对于实现精准灌溉、提高作物抗逆性和产量等具有重要意义。为优化夏玉米水分胁迫诊断方法和提高诊断精度,该研究以夏玉米为对象,利用无人机搭载六通道多光谱传感器获取2022年夏玉米拔节期和抽雄期的遥感影像数据,且同步采集夏玉米气孔导度和表型参数数据,监督分类剔除冗余背景后使用灰度共生矩阵计算得到冠层植被指数和图像纹理信息,通过贝叶斯信息准则和全子集筛选法筛选出敏感的植被指数、图像纹理和表型参数及其组合,结合极限学习机、随机森林和反向传播神经网络3种机器学习方法构建夏玉米气孔导度预估模型,并基于最优气孔导度预估模型绘制夏玉米水分胁迫状况反演图。结果表明,多光谱图像的夏玉米冠层反射率与气孔导度呈弱负相关,植被指数和表型参数与气孔导度呈极显著正相关,不同波段的图像纹理均与气孔导度有较高的相关性,其中550 nm波段最佳。植被指数用于评估植被整体健康和水分状况,图像纹理用于捕捉作物空间分布、纹理和结构特征,表型参数用于立体反映作物生理和形态信息,它们在诊断作物水分胁迫的机理上具有互补性。基于植被指数、图像纹理和表型参数构建的反向传播神经网络模型是夏玉米水分胁迫诊断的最佳模型（决定系数为0.841,均方根误差为0.043 mol/(m²·s),平均绝对误差为0.034 mol/(m²·s) ）,并显著改善了对气孔导度较低值的低估情况。绘制的夏玉米水分胁迫状况反演图呈现出广泛的应用潜力,能够便捷准确地诊断作物水分胁迫状况,以优化灌溉策略,调整资源分配。研究结果可为夏玉米的水分胁迫诊断提供一种可行而准确的方法。     

Estimating the local mean for Bayesian maximum entropy by generalized least squares and maximum likelihood, and an application to the spatial analysis of a censored soil variable

The Bayesian maximum entropy (BME) method is a valuable tool, with rigorous theoretical underpinnings, with which to predict with soft (imprecise) data. The methodology uses a general knowledge base to derive a joint prior distribution of the data and the prediction by the criterion of maximum entropy; the hard (precise) and soft data are then processed using this prior distribution to yield a posterior distribution that provides the BME prediction. The general knowledge base commonly consists of the mean and covariance functions, which may be extracted from the data. The common method for extracting the mean function from the data is a generalized least squares (GLS) approach. However, when the soft data take the form of intervals of plausible values, this method can result in errors in the BME predictions. This paper suggests a maximum likelihood (ML) method for fitting the local mean. The two methods are compared in terms of their predictions, firstly on simulated random fields and then on a case study to predict the depth of soil using some censored data. The results show that the ML method can result in more accurate BME predictions; the degree of improvement over the GLS method depends on the parameters of the spatial covariance model.     

Bayesian estimation of cluster-level test accuracy based on different sampling schemes

We develop Bayesian models to estimate cluster-level test characteristics, sensitivity, specificity, prevalence, and predictive values, based on four different sampling schemes: a single test case and three sequential test cases. The corresponding cluster-level characteristics are calculated and compared for different sample sizes, sampling schemes, individual-level sensitivities, specificities, and cut-off values. We compared posterior estimates of individual-level and cluster-level characteristics for these four sampling schemes with simulated data. Two illustrations, one for Johne’s disease in cattle and another for Salmonella in pig herds, are used to demonstrate application of the methods.     

作物生长模型与定量遥感参数结合研究进展与展望

作物生长模型与定量遥感参数的结合,不仅满足前者实现区域应用的需求,也有助于提高后者的反演精度,在生态、农业、资源调查与全球气候变化等研究上意义重大。该文从作物生长模型空间应用拓展的角度,对国内外主流作物生长模型、定量遥感参数以及两者结合的参数与方法进行了概述,分析了典型作物生长模型的主要模拟过程及其驱动、初始化、输出等参数,总结了当前定量遥感正反演结果可为作物生长模型区域应用提供的参数数据;建立了作物生长模型模拟过程与定量遥感参数的对应关系,对比分析了作物生长模型与定量遥感参数的不同结合方式。基于以上内容,对作物生长模型面应用的限制因素及其与定量遥感参数的关系、作物生长模型面应用时参数尺度效应的影响、作物生长模型与定量遥感参数耦合方法的发展3个方面展开了讨论,以期为作物生长模型与定量遥感参数开展更好的结合研究提供参考。     

Exploring scale‐dependent correlation of soil properties by nested sampling

The value of nested sampling for exploring the spatial structure of univariate variation of the soil has been demonstrated in several studies and applied to practical problems. This paper shows how the method can be extended to the multivariate case. While the extension is simple in theory, in practice the direct estimation of covariance components by equating mean‐square matrices with their expectation will often lead to estimates that are not positive semidefinite. This paper discusses solutions to this problem for balanced and unbalanced sample designs. In the balanced case there is a residual maximum likelihood (REML) estimator that will find estimates of covariance components that maximize an overall likelihood on the condition that all components are positive semidefinite (p.s.d.). This is possible because the condition is met if the differences of successive mean‐square matrices are positive semidefinite, and this constraint can be incorporated into an algorithm. This does not hold for unbalanced designs. In this paper the problem was solved for unbalanced designs by scaling covariance components that were not p.s.d. to the nearest p.s.d. matrix according to a Euclidean distance. These methods were applied to data from three surveys, two with balanced and one with unbalanced sampling. Different patterns of scale‐dependence of the correlation of soil properties were found. For example, at Ginninderra Experimental Station in Australia the soil water content and bulk density were correlated significantly, with the correlation increasing with distance to 56 m, but at longer distances the properties were not significantly correlated. By contrast, the pH of the soil and the available P content showed correlation that increased with distance. The implications of these results for planning more detailed sampling, both for prediction and for investigation of processes, are discussed.     

A Bayesian Approach to Spatial Prediction With Flexible Variogram Models

A Bayesian approach to covariance estimation and spatial prediction based on flexible variogram models is introduced. In particular, we consider black-box kriging models. These variogram models do not require restrictive assumptions on the functional shape of the variogram; furthermore, they can handle quite naturally non isotropic random fields. The proposed Bayesian approach does not require the computation of an empirical variogram estimator, thus avoiding the arbitrariness implied in the construction of the empirical variogram itself. Moreover, it provides a complete assessment of the uncertainty in the variogram estimation. The advantages of this approach are illustrated via simulation studies and by application to a well known benchmark dataset.     

Residual Variance–Covariance Modelling in Analysis of Multivariate Data from Variety Selection Trials

Field trials for variety selection often exhibit spatial correlation between plots. When multivariate data are analysed from these field trials, there is the added complication in having to simultaneously account for correlation between the traits at both the residual and genetic levels. This may be temporal correlation in the case of multi-harvest data from perennial crop field trials, or between-trait correlation in multi-trait data sets. Use of parsimonious yet plausible models for the variance–covariance structure of the residuals for such data is a key element to achieving an efficient and inferentially sound analysis. In this paper, a model is developed for the residual variance–covariance structure firstly by considering a multivariate autoregressive model in one spatial direction and then extending this to two spatial directions. Conditions for ensuring that the processes are directionally invariant are presented. Using a canonical decomposition, these directionally invariant processes can be transformed into a set of independent separable processes. This simplifies the estimation process. The new model allows for flexible modelling of the spatial and multivariate interaction and allows for different spatial correlation parameters for each harvest or trait. The methods are illustrated using data from lucerne breeding trials at several environments.     

基于全局敏感性分析和贝叶斯方法的WOFOST作物模型参数优化

作物模型参数的敏感性分析、标定和验证可以提高模型的效率和精准度,进而为模型应用做好准备工作。该研究结合参数全局敏感性分析方法以及贝叶斯后验估计理论的马尔科夫蒙特卡洛(Markov Chain Monte Carlo,MCMC)方法,以华北栾城站三年的冬小麦观测数据(叶面积和地上生物量)为参照,对WOFOST模型的55个品种参数进行了敏感性分析、筛选和优化。发现:1)对叶面积影响较大的参数为:生育期为0、0.5、0.6和0.75时的比叶面积、生育期为1.5时的最大光合速率、叶面积指数最大增长率;对地上干物质影响较大的参数为:生育期为1.5时的最大光合速率、生育期为0时的比叶面积、35℃时叶面积的生命周期、生育期为0时的散射消光系数、生育期为1.8时的最大光合速率、储存器官的同化物转换效率。2)潜在和雨养产量水平下,最大叶面积和地上生物量对参数的敏感性差异不大。3)马尔科夫蒙特卡洛方法(MCMC)可以对WOFOST模型品种参数较好地优化;设计的3种校正-验证方案中,第1种方案(用1998-1999年作为校正年份,1999-2000年,2000-2001年作为验证年份)模拟效果最好。4)优化后的参数,模型对潜在产量水平模拟较好,一致性指数均大于0.9,相对均方根误差小于20%;而对有水分胁迫的雨养情况下比潜在产量水平的模拟结果差,表明模型对水分胁迫的模拟不足。该研究为WOFOST模型区域应用和模型调整优化提供科学理论依据。     

Transformations in mixed models: Application to risk analysis for a multienvironment trial

An important trait in crop cultivar evaluation is stability of performance across environments. There are many different measures of stability, most of which are related to variance components of a mixed model. We believe that stability measures assessing yield risk are of particular relevance, because they integrate location and scale parameters in a meaningful way. A prerequisite for obtaining valid risk estimates is an appropriate model for the distribution of yield across environments. Multienvironment trials (MET) are often analyzed by mixed linear models, assuming that environments are a random sample from a target population, and that random terms in the model are normally distributed. The normality assumption may not always be tenable, and consequently, risk estimates may be biased. In this article, we suggest a transformation approach based on the Johnson system to cope with nonnormality in mixed models. The methods are exemplified using an international wheat yield trial. The importance of accounting for nonnormality in risk analyses based on MET is emphasized. We suggest that transformations should be routinely considered in analyses to assess risk.     

基于MCMC方法的WOFOST模型参数标定与不确定性分析

为探究作物生长模型参数的自动标定技术及其不确定性分析方法,该研究以郑州农业气象试验站为试验点,利用融入了snooker更新(snooker update)的DE-MC(differential evolution Markov chain,差分进化马尔科夫链)方法实现对WOFOST(world food studies)作物生长模型的参数标定和不确定性定量评价。snooker更新增加了DE-MC算法中候选样本的多样性,从而实现利用更少的并行链对多维参数空间进行有效采样,较适合于WOFOST模型参数众多的特性。结果表明:相比于模型默认值,采用MCMC(Markov chain Monte Carlo,马尔科夫链-蒙特卡洛)标定后的参数,叶面积指数(leaf area index,LAI)模拟精度可提高51.40%~53.07%,产量模拟精度提高8.25%~8.88%。标定参数中,SPAN、SLATB070、SLATB040、AMAXTB130和SLATB00的后验分布可近似为高斯分布,其中SPAN的不确定性最低。带入后验参数集合进行模型,LAI在三叶期至返青期之间以及拔节期至抽穗期之间模拟的不确定性较大;产量模拟的不确定性随时间不断增大,至乳熟期前后达到稳定。该方法能够实现对多参数复杂作物生长模型的参数标定和不确定性分析,对作物模型参数估计及提高模拟精度具有重要作用。     

Spatial designs and properties of spatial correlation: Effects on covariance estimation

In a spatial regression context, scientists are often interested in a physical interpretation of components of the parametric covariance function. For example, spatial covariance parameter estimates in ecological settings have been interpreted to describe spatial heterogeneity or “patchiness” in a landscape that cannot be explained by measured covariates. In this article, we investigate the influence of the strength of spatial dependence on maximum likelihood (ML) and restricted maximum likelihood (REML) estimates of covariance parameters in an exponential-with-nugget model, and we also examine these influences under different sampling designs—specifically, lattice designs and more realistic random and cluster designs—at differing intensities of sampling (n=144 and 361). We find that neither ML nor REML estimates perform well when the range parameter and/or the nugget-to-sill ratio is large—ML tends to underestimate the autocorrelation function and REML produces highly variable estimates of the autocorrelation function. The best estimates of both the covariance parameters and the autocorrelation function come under the cluster sampling design and large sample sizes. As a motivating example, we consider a spatial model for stream sulfate concentration.     

The behaviour of soil process models of ammonia volatilization at contrasting spatial scales

Process models are commonly used in soil science to obtain predictions at a spatial scale that is different from the scale at which the model was developed, or the scale at which information on model inputs is available. When this happens, the model and its inputs require aggregation or disaggregation to the application scale, and this is a complex problem. Furthermore, the validity of the aggregated model predictions depends on whether the model describes the key processes that determine the process outcome at the target scale. Different models may therefore be required at different spatial scales. In this paper we develop a diagnostic framework which allows us to judge whether a model is appropriate for use at one or more spatial scales both with respect to the prediction of variations at those scale and in the requirement for disaggregation of the inputs. We show that spatially nested analysis of the covariance of predictions with measured process outcomes is an efficient way to do this. This is applied to models of the processes that lead to ammonia volatilization from soil after the application of urea. We identify the component correlations at different scales of a nested scheme as the diagnostic with which to evaluate model behaviour. These correlations show how well the model emulates components of spatial variation of the target process at the scales of the sampling scheme. Aggregate correlations were identified as the most pertinent to evaluate models for prediction at particular scales since they measure how well aggregated predictions at some scale correlate with aggregated values of the measured outcome. There are two circumstances under which models are used to make predictions. In the first case only the model is used to predict, and the most useful diagnostic is the concordance aggregate correlation. In the second case model predictions are assimilated with observations which should correct bias in the prediction, and errors in the variance; the aggregate correlations would be the most suitable diagnostic.     

Predicting Carbon Stocks Following Reforestation of Pastures: A Sampling Scenario‐Based Approach for Testing the Utility of Field‐Measured and Remotely Derived Variables

Reforestation of agricultural lands is an important means of restoring land and sequestering carbon (C). At large scales, the labour and costs of direct measurement of ecosystem responses can be prohibitive, making the development of models valuable. Here, we develop a new sampling scenario‐based modelling approach coupled with Bayesian model averaging to build predictive models for absolute values in mixed‐species woody plantings and differences from their adjacent pasture, for litter stocks, soil C stocks and soil C:N ratios. Modelling scenarios of increasing data availability and effort were tested. These included variables that could be derived without a site visit (e.g. location, climate and management) that were sampled in the adjacent pasture (e.g. soil C and nutrients) or were sampled in the environmental planting (e.g. vegetation, litter properties, soil C and nutrients). The predictive power of models varied considerably among C variables (litter stocks, soil C stocks and soil C:N ratios in tree plantings and their differences to their adjacent pastures) and the model scenarios used. The use of a sampling scenario‐based approach to building predictive models shows promise for monitoring changes in tree plantings, following reforestation. The approach could also be readily adapted to other contexts where sampling effort for predictor variables in models is a major potential limitation to model utilization. This study demonstrates the benefit of exploring scenarios of data availability during modelling and will be especially valuable where the sampling effort differs greatly among variables. Copyright © 2016 John Wiley & Sons, Ltd.     

Evaluating the performance of a block updating MCMC sampler in a simple genetic application

Markov chain Monte Carlo (MCMC) methods have provided an enormous break-through in the analysis of large complex problems such as those which frequently arise in genetic applications. The richness of the inference and the flexibility of an MCMC Bayesian approach in terms of design, data structure that can be analyzed, and models that can be posed, is indisputable. However, despite the strengths of the Bayesian approach, it is important to acknowledge that there are other, often easier, ways of tackling a problem. This is so, especially when simpler, qualitative answers are sought, such as presence or absence of a quantitative trait locus. We critically evaluate the behavior of a Bayesian aCMC block sampler for the detection of a quantitative trait locus by linkage with marker data, and compare it with a traditional least squares method. Some practical issues are illustrated by discussing the pros and cons of a Bayesian block updating sampling scheme versus the least squares method in the context of a simple genetic mapping problem. Depending on the focus of analysis, we show that the MCMC sampler does not always outperform the simpler approach from a frequentist perspective, and, more to the point, may not always perform appropriately in any particular replication.     

Bayesian spatial modeling of data from avian point count surveys

We present a unified framework for modeling bird survey data collected at spatially replicated survey sites in the form of repeated counts or detection history counts, through which we model spatial dependence in bird density and variation in detection probabilities due to changes in covariates across the landscape. The models have a complex hierarchical structure that makes them suited to Bayesian analysis using Markov chain Monte Carlo (MCMC) algorithms. For computational efficiency, we use a form of conditional autogressive model for modeling spatial dependence. We apply the models to survey data for two bird species in the Great Smoky Mountains National Park. The algorithms converge well for the more abundant and easily detected of the two species, but some simplification of the spatial model is required for convergence for the second species. We show how these methods lead to maps of estimated relative density which are an improvement over those that would follow from past approaches that ignored spatial dependence. This work also highlights the importance of good survey design for bird species mapping studies.     

Investigating flow mechanisms in a forest soil by mixed‐effects modelling

Uniform and preferential flow produces typical infiltration patterns. We made three tracer experiments in a Norway spruce forest soil and qualitatively identified the dominant flow regime based on stained patterns. We analysed soil texture, fine root density and soil bulk density from preferential flow paths and the soil matrix by means of linear mixed‐effects models. These models can account for dependences in the data structure caused by hierarchical sampling and can deal with missing values. There were between 44% (topsoil) and 76% (subsoil) larger root densities in preferential flow paths than in the soil matrix. No significant differences in soil texture were detected. The bulk density was greater in the soil matrix by 0.12 g cm⁻³, which is probably because of a greater soil organic matter content of preferential flow paths. Using flow patterns and model results we identified the dominant flow mechanisms. At this study site, roots constituted the main preferential flow paths and induced macropore flow, especially in the topsoil. In the subsoil, root density decreased and inhomogeneous infiltration from preferential flow paths into the soil matrix caused unstable flow.