Combining Survey and Non-survey Data for Improved Sub-area Prediction Using a Multi-level Model

Combining information from different sources is an important practical problem in survey sampling. Using a hierarchical area-level model, we establish a framework to integrate auxiliary information to improve state-level area estimates. The best predictors are obtained by the conditional expectations of latent variables given observations, and an estimate of the mean squared prediction error is discussed. Sponsored by the National Agricultural Statistics Service of the US Department of Agriculture, the proposed model is applied to the planted crop acreage estimation problem by combining information from three sources, including the June Area Survey obtained by a probability-based sampling of lands, administrative data about the planted acreage and the cropland data layer, which is a commodity-specific classification product derived from remote sensing data. The proposed model combines the available information at a sub-state level called the agricultural statistics district and aggregates to improve state-level estimates of planted acreages for different crops. Supplementary materials accompanying this paper appear on-line.     

Estimating the Risk of a Crop Epidemic From Coincident Spatio-temporal Processes

Fusarium Head Blight (FHB), or “scab,” is a very destructive disease that affects wheat crops. Recent research has resulted in accurate weather-driven models that estimate the probability of an FHB epidemic based on experiments. However, these predictions ignore two crucial aspects of FHB epidemics: (1) An epidemic is very unlikely to occur unless the plants are flowering, and (2) FHB spreads by its spores, resulting in spatial and temporal dependence in risk. We develop a new approach that combines existing weather-based probabilities with information on flowering dates from survey data, while simultaneously accounting for spatial and temporal dependence. Our model combines two space-time processes, one associated with pure weather-based FHB risks and the other associated with flowering date probabilities. To allow for scalability, we model spatiotemporal dependence via a process convolutions approach. Our sample-based approach produces a realistic assessment of areas that are persistently at high risk (where the probability of an epidemic is elevated for extended time periods), along with associated estimates of uncertainty. We conclude with the application of our approach to a case study from North Dakota.     

Bayesian Hierarchical Analysis for Multiple Health Endpoints in a Toxicity Study

Bayesian hierarchical models are built to fit multiple health endpoints from a dose-response study of a chemical contaminant, perchlorate. Perchlorate exposure results in iodine uptake inhibition in the thyroid, with health effects manifested by changes in blood hormone concentrations and histopathological effects on the thyroid. We propose empirical models to fit blood hormone concentration and thyroid histopathology data for rats exposed to perchlorate in the 90-day study of Springborn Laboratories Inc. (1998), based upon a mechanistic model derived from the assumed toxicological relationships between dose and the various endpoints. All of the models are fit in a Bayesian framework, and predictions about each endpoint in response to dose are simulated based on the posterior predictive distribution. A hierarchical model tries to exploit possible similarities between different combinations of sex and exposure duration, and it allows us to produce more stable estimates of dose-response curves. We also illustrate how the Bayesian model specification allows us to address additional questions that arise after the analysis.     

Hierarchical modeling of cluster size in wildlife surveys

Clusters or groups of individuals are the fundamental unit of observation in many wildlife sampling problems, including aerial surveys of waterfowl, marine mammals, and ungulates. Explicit accounting of cluster size in models for estimating abundance is necessary because detection of individuals within clusters is not independent and detectability of clusters is likely to increase with cluster size. This induces a cluster size bias in which the average cluster size in the sample is larger than in the population at large. Thus, failure to account for the relationship between detectability and cluster size will tend to yield a positive bias in estimates of abundance or density. I describe a hierarchical modeling framework for accounting for cluster-size bias in animal sampling. The hierarchical model consists of models for the observation process conditional on the cluster size distribution and the cluster size distribution conditional on the total number of clusters. Optionally, a spatial model can be specified that describes variation in the total number of clusters per sample unit. Parameter estimation, model selection, and criticism may be carried out using conventional likelihood-based methods. An extension of the model is described for the situation where measurable covariates at the level of the sample unit are available. Several candidate models within the proposed class are evaluated for aerial survey data on mallard ducks (Anas platyrhynchos).     

Adaptive sampling and reconnaissance surveys for geostatistical mapping of the soil

The effort required to survey a soil variable depends upon the acceptable uncertainty of estimates and the variogram of the variable. The variogram is unknown prior to sampling, so it must be inferred from a reconnaissance survey before an efficient survey can be designed. The results of reconnaissance surveys are subject to uncertainty, which depends upon the variogram and the number and location of observations. Here, we develop an adaptive approach for optimizing reconnaissance surveys. The observations within these reconnaissance surveys are collected in distinct phases. After each phase, a probability density function of the required sampling density of the main survey is calculated within a Bayesian framework. The number and location of observations within further phases are selected to reduce efficiently the uncertainty of the estimate of the required sampling density. In simulation studies, the number and location of observations in Bayesian adaptive reconnaissance surveys vary according to the variogram of the property of interest. For variograms with a short range, the reconnaissance surveys are intensive with a large proportion of clustered locations. Fewer, more evenly spread locations are required for variables with a long range. Bayesian adaptive reconnaissance surveys lead to more efficient surveys than conventional approaches because the reconnaissance survey is specifically designed for the variable of interest. A hand‐held field system is implemented and tested in a survey of soil moisture content over a field.     

Hierarchical models of animal abundance and occurrence

Much of animal ecology is devoted to studies of abundance and occurrence of species, based on surveys of spatially referenced sample units. These surveys frequently yield sparse counts that are contaminated by imperfect detection, making direct inference about abundance or occurrence based on observational data infeasible. This article describes a flexible hierarchical modeling framework for estimation and inference about animal abundance and occurrence from survey data that are subject to imperfect detection. Within this framework, we specify models of abundance and detectability of animals at the level of the local populations defined by the sample units. Information at the level of the local population is aggregated by specifying models that describe variation in abundance and detection among sites. We describe likelihood-based and Bayesian methods for estimation and inference under the resulting hierarchical model. We provide two examples of the application of hierarchical models to animal survey data, the first based on removal counts of stream fish and the second based on avian quadrat counts. For both examples, we provide a Bayesian analysis of the models using the software WinBUGS.     

WOFOST模型的发展及应用

作物生长模拟模型已经成为一门新兴的科学,可以为农业资源的管理利用、农业最大收益的获取提供科学的依据。WOFOST(W orld Food Stud ies)模型是荷兰瓦根宁农业大学和世界粮食研究中心共同开发研制的,是模拟特定的土壤和气候条件下一年生作物生长的动态的、解释性模型。WOFOST模型已经在欧洲、非洲以及亚洲的一些地区得到了运用和验证,可用于水稻、玉米、小麦等多种一年生作物的模拟。WOFOST模型可用来分析作物产量风险,不同年份产量的变化,土壤类型及气候变化对产量变化的影响;确定播种策略以及农业机械使用的关键时期;该模型还可用于估计某种作物最大潜在产量,提高灌溉和施肥的增产效益,对生长在不利条件以及地区的作物产量进行预测等。该模型对可持续农业的发展具有积极的指导作用。     

Cost-effective abundance estimation of rare animals: Testing performance of small-boat surveys for killer whales in British Columbia

Top predators are often rare, subject to anthropogenic mortality, and possess life-history traits that make them inherently vulnerable to extinction. IUCN criteria recognise populations as Critically Endangered when abundance is <250 mature individuals, but estimating abundance of rare species can be more challenging than for common ones. Cost-effective methods are needed to provide robust abundance estimates. In marine environments, small boats are more widely accessible than large ships for researchers conducting sightings surveys with limited funds, but studies are needed into efficacy of small-boat surveys. This study compares line transect and mark-recapture estimates from small-boat surveys in summer 2004 and 2005 for ‘northern resident’ killer whales in British Columbia to true population size, known from censuses conducted by Fisheries and Oceans Canada. The line transect estimate of 195 animals (95% CI 27-559) used model averaging to incorporate uncertainty in the detection function, while the mark-recapture estimate of 239 animals (CI 154-370) used a simple two-sample Chapman estimator. Both methods produced estimates close to the true population size, which numbered 219 animals in 2004 and 235 in 2006, but both suffered from the small sample sizes and violations of some model assumptions that will vex most pilot studies of rare species. Initial abundance estimates from relatively low-cost surveys can be thought of as hypotheses to be tested as new data are collected. For species of conservation concern, any cost-effective attempt to estimate absolute abundance will assist status assessments, as long as estimates are presented with appropriate caveats.     

Using seasonal climate forecasts to improve maize production decision support in Zimbabwe

Maize production in marginal tropical regions is at great risk due to rainfall variability and climate change. Climate change is set to increase the variability and uncertainty of inter-annual rainfall. Farmers who depend on rainfed maize production for their livelihoods would therefore benefit from improved climate based forecasting of production likelihood. In this study we developed a simple maize production decision support tool for Masvingo by using seasonal climate forecasts and a crop model to forecast maize yields likelihood prior to the season. We follow up on earlier studies carried out in Zimbabwe which show that the El Nino Southern Oscillation (ENSO) can be used to forecast rainfall and maize yields in Zimbabwe. An ENSO based seasonal climate analysis tool (RAINMAN) was used to produce probabilistic monthly climate forecasts for Masvingo corresponding to the phases of the Southern Oscillation Index (SOI). The climate forecasts were used to run a crop model (AquaCrop) for a variety of scenarios relevant to maize production (monthly rainfall, cultivar selection, planting date, and fertility level). The results of the simulations were similar to those observed by Phillips et al. (1997) and formed the basis for the development of an operational decision support tool. Simulated maize yields varied from 1.2 t/ha to 5.8 t/ha. The simulated yields were higher than expected average yields in a marginal region like Masvingo especially under small holder farming. The work suggested that optimal use of forecasts may lead to improved maize production in Masvingo. The study set a platform for the development of operational climate based maize production decision support tools in Zimbabwe.     

A Bayesian Model for Presence-Only Semicontinuous Data,With Application to Prediction of Abundance of <Emphasis Type="Italic">Taxus Baccata</Emphasis> in Two Italian Regions

In studies about the potential distribution of ecological niches, only the presence of the species of interest is usually recorded. Pseudo-absences are sampled from the study area in order to avoid biased estimates and predictions. For cases in which, instead of the mere presence, a continuous abundance index is recorded, we derive a two-part model for semicontinuous (i.e., positive with excess zeros) data which explicitly takes into account uncertainty about the sampled zeros. Our model is a direct extension of the one of Ward et al. (Biometrics 65, 554–563, 2009). It is fit in a Bayesian framework, which has many advantages over the maximum likelihood approach of Ward et al. (2009), the most important of which is that the prevalence of the species does not need to be known in advance. We illustrate our approach with real data arising from an original study aiming at the prediction of the potential distribution of the Taxus baccata in two central Italian regions. Supplemental materials giving detailed proofs of propositions, tables and code are available online.     

The Matérn variogram model: Implications for uncertainty propagation and sampling in geostatistical surveys

The Matérn variogram model has been advocated because it is flexible and can represent varied behaviour at small lags. We show how the constraints on the spherical and exponential variogram at short lags ignore a possible source of uncertainty in the variogram and so in kriging surveys, that the Matérn model can describe. Matérn, spherical and exponential variogram models were fitted by maximum likelihood to a set of log₁₀(K) observations made on a regular grid at Broom's Barn Farm, Suffolk, England. The likelihood profiles of the Matérn parameter estimates were asymmetric. Thus the uncertainty of these estimates could only be adequately assessed by a Bayesian approach. The uncertainty of estimated parameters of the Matérn variogram was larger than for the exponential variogram. This is an indication that the assumption of an exponential model limits the behaviour that may be described by the variogram. Thus uncertainty analyses where an exponential variogram is assumed may underestimate the uncertainty of kriged estimates. Bayesian analysis of the kriged estimates of log₁₀(K) at Broom's Barn Farm using the Matérn variogram revealed an observable component of uncertainty due to variogram uncertainty. When an exponential variogram model was used, the estimate of this component of uncertainty was negligible. The Matérn variogram should therefore be used rather than the exponential model when assessing the adequacy of a variogram estimate. A method of designing sample schemes which is suitable for both estimating a Matérn variogram and interpolation is suggested.     

Transformation of a nonnormal distribution of quantitative traits for breeding purposes

Journal of Agricultural, Biological and Environmental Statistics - Some continuous quantitative traits such as yield are not always normally distributed. This article proposes an underlying normal...     

Spatial models for line transect sampling

This article develops methods for fitting spatial models to line transect data. These allow animal density to be related to topographical, environmental, habitat, and other spatial variables, helping wildlife managers to identify the factors that affect abundance. They also enable estimation of abundance for any subarea of interest within the surveyed region, and potentially yield estimates of abundance from sightings surveys for which the survey design could not be randomized, such as surveys conducted from platforms of opportunity. The methods are illustrated through analyses of data from a shipboard sightings survey of minke whales in the Antarctic.     

Measuring uncertainty in estimates of biodiversity loss: The example of biodiversity intactness variance

Developing adequate indicators of biodiversity change is an urgent task for biodiversity studies and policy. An important component of any indicator is a measure of the uncertainty in the estimates it produces. In this paper, we derive the biodiversity intactness variance (BIV) as a formal measure of uncertainty to accompany the recently developed biodiversity intactness index (BII) (Scholes and Biggs [Scholes, R.J., Biggs, R., 2005. A biodiversity intactness index. Nature 434, 45–49]). The BII is based on estimates of baseline species richness, the area of different land-uses, and the abundance of different species under different land uses. The BIV quantifies uncertainty in the abundance estimates, which are the main source of uncertainty in BII. The BII for southern Africa in the year 2000 has been estimated at 84.4%. We calculate the accompanying BIV at 50.4, providing a 95% confidence interval of 76.6–92.2% for BII. By applying the BIV, we can quantify the major sources of uncertainty in the BII for southern Africa: they stem from the abundance estimates for mammals and birds, and for savanna regions and degraded areas. The BIV therefore provides a means for better assessing the state of biodiversity loss and for highlighting research priorities.     

Neural network imputation: An experience with the national resources inventory survey

Imputation is needed in almost all major surveys. Imputation tools are often adopted according to the convenience and the contexts of the surveys. Traditional hot-deck imputation needs extensive knowledge of the survey variables. Explicit model-based imputation needs a valid model for every survey variable. In large-scale national surveys, different groups of people with different backgrounds work on different stages of surveys and often the statistical estimation group has little or insufficient communication with the other groups. In such situations, it is difficult to use hot-deck imputation. On the other hand, because of the complex nature of the survey, finding a suitable model for every survey variable may not be easy and thus a nonparametric method— such as neural network imputation—may be attractive. One such large-scale national survey is the U.S. Department of Agriculture’s National Resources Inventory Survey (NRI). By design, the survey has missing values. The missing values are imputed using a donor-based method. This article develops a neural network imputation model and compares its performance with that of the existing imputation method. The end result looks promising.     

基于植被初级生产力的农用地理论和可实现产能核算研究

为解决传统基于农用地分等成果计算农用地理论产能和可实现产能时遇到的问题,本文将植被初级生产力(NPP)测算应用于农用地产能核算。以湖北省武汉市为研究区,运用CASA模型测算研究区农用地NPP,通过样点调查分别建立NPP与农用地理论单产和可实现单产的线性回归模型,在此基础上进行农用地理论产能和可实现产能核算。通过核算得到研究区75个乡镇的农用地理论产能及单产和可实现产能及单产,理论和可实现产能较大的乡镇主要分布在研究区北部及东南部地区,理论和可实现单产较大的乡镇则主要分布在研究区西部和东北地区,而靠近主城区周边乡镇的理论和可实现产能及单产均较低。将核算结果与传统方法计算得到的农用地产能核算成果进行对比分析,发现两种方法的核算成果在乡镇理论和可实现产能分布上非常接近,具有较高一致性;但在乡镇理论单产和可实现单产分布上并不完全一致。研究结果表明基于NPP测算的农用地产能核算方法是可行的,该方法避免了传统核算方法资料收集繁琐,主观性强等不足,且不以农用地分等定级成果为基础,可实现农用地产能快速核算。     

不同气候区和不同产量水平下APSIM-Wheat模型的参数全局敏感性分析

量化作物模型的参数敏感性和模拟结果的不确定性对模型的标定和应用具有重要意义。为了探讨小麦生长模型(APSIM-Wheat)在不同气候区和不同产量水平下参数的敏感性,以及由于参数造成模拟结果的不确定性,以华北栾城、黄土高原长武、四川盐亭和新疆乌兰乌苏4个不同气候区下的典型冬小麦生产地为分析对象,运用扩展傅里叶幅度检验法(extended Fourier amplitude sensitivity test,EFAST)的全局敏感性分析方法,量化了小麦生长模型(APSIM-Wheat模型)在3种产量水平下(潜在、雨养和实际产量)的开花期、成熟期、产量、生育期的蒸散(evapotranspiration,ET)对品种、土壤和生化等33个参数的敏感性和不确定性。发现:1影响开花期和成熟期较为敏感的参数依次是:始花期积温、出苗到拔节积温、春化指数、光周期因子、灌浆期积温;2影响产量较敏感的参数依次为:春化指数、出苗到拔节积温、每茎谷粒质量、潜在灌浆速率、光周期指数、最大谷粒质量和辐射利用效率(radiation use efficiency,RUE);影响生育期蒸散较为敏感的参数依次为:春化指数、出苗到拔节积温、光周期指数、始花期积温;3不同产量水平下,参数敏感性差异不大,4个不同气候类型下的冬小麦开花期、成熟期、产量和生育期的蒸散对参数的敏感性基本一致;4不同气候区下,开花期和成熟期对模型参数敏感性差异很小,但产量和生育期的蒸散对参数敏感性有差异。该研究为APSIM-Wheat模型的区域应用和模型调参提供了科学指导依据。     

Comparison of dry deposition velocities for SO2, HNO3 and SO4 2− estimated with two inferential models

Dry deposition velocity estimates of SO, HNO₃ and SO₄ ^2? were computed for six locations in eastern North America using two different inferential models; a Big-Leaf model utilized by the U. S. National Dry Deposition Network (NDDN) and, a land-use based model (LUM) that has been used in the past to estimate the relative importance of dry versus wet deposition over selected Canadian regions. There were consistent differences between models that were related to the surface type, chemical species and time of year. Mean monthly dry deposition velocities based upon the 1990–91 time period were compared at two locations. The seasonal cycles in deposition velocity were similar between models, but there were considerable differences in the amplitude of the cycles. The LUM predicted about a 400% increase in S042- deposition velocity from the winter to the summer months, while there was a 50 to 100% increase in the NDDN model estimates, depending upon location. According to the LUM, HN03 deposition to crop land increased by about a factor of 6 from winter to summer, while the big leaf model predicted a 50% increase. Overall, there was better agreement for SO₂. Averaged over 12 months, the differences in deposition velocity between models were smaller and generally within the range of uncertainty associated with inferential models. For all six sites, the mean percent difference between models in deposition velocity for SO₂, HNO₃ and SO₄ ^2? were 13, 35 and 79, respectively. These differences highlight the effect of using different methods for estimating dry deposition and the importance of applying the same model when examining regional patterns in dry/total deposition rates.     

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.     

Verifying Reification With Application to a Rainfall–Runoff Computer Simulator

Deterministic computer models or simulators are used regularly to assist researchers in understanding the behavior of complex physical systems when real-world observations are limited. However, simulators are often imperfect representations of physical systems and may introduce layers of uncertainty into model-based inferences that are hard to quantify. To formalize the use of expert judgment in assessing simulator uncertainty, Goldstein and Rougier in J. Stat. Plan. Inference 139:1221–1239 (2009) propose a method, called reification, that decomposes the discrepancy between simulator predictions and reality by an improved, hypothetical computer model known as a “reified simulator”. One criticism of reification is that validation is, at best, challenging; only expert critiques can validate the subjective judgments used to specify a reified simulator. For this paper, we develop a procedure to quantify the advantages of reification for fast, modular simulators. The procedure is explained and implemented within the context of a rainfall-runoff that was developed by Iorgulescu, Beven, and Musy in Hydrol. Process. 19:2557–2573 (2005). We show that reification leads to informed judgments of simulator uncertainty