Modeling Complex Spatial Dependencies: Low-Rank Spatially Varying Cross-Covariances With Application to Soil Nutrient Data

Advances in geo-spatial technologies have created data-rich environments which provide extraordinary opportunities to understand the complexity of large and spatially indexed data in ecology and the natural sciences. Our current application concerns analysis of soil nutrients data collected at La Selva Biological Station, Costa Rica, where inferential interest lies in capturing the spatially varying relationships among the nutrients. The objective here is to interpolate not just the nutrients across space, but also associations among the nutrients that are posited to vary spatially. This requires spatially varying cross-covariance models. Fully process-based specifications using matrix-variate processes are theoretically attractive but computationally prohibitive. Here we develop fully process-based low-rank but non-degenerate spatially varying cross-covariance processes that can effectively yield interpolate cross-covariances at arbitrary locations. We show how a particular low-rank process, the predictive process, which has been widely used to model large geostatistical datasets, can be effectively deployed to model non-degenerate cross-covariance processes. We produce substantive inferential tools such as maps of nonstationary cross-covariances that constitute the premise of further mechanistic modeling and have hitherto not been easily available for environmental scientists and ecologists.     

ALMANAC作物模型参数的敏感性分析

为了方便模型数据库的组建,降低模拟结果的不确定性,本文根据山东禹城综合试验站2000-2003年的田间试验资料,进行AL-MANAC模型模拟冬小麦和夏玉米的验证。在此基础上采用OTA（即每次只改变其中1个参数）方法,对模型的土壤参数和作物参数进行敏感性分析。验证结果表明,ALMANAC模型能够较好地模拟冬小麦和夏玉米的产量和叶面积指数的动态变化,冬小麦和夏玉米模拟产量的相对误差（RE）为-8.6%~6.0%、-3.5%~7.2%,叶面积指数的RE为-13.1%~14.8%、-13.0%~12.2%;敏感性分析显示,土壤参数中的径流曲线数、土壤容重、田间持水量和土层厚度对模拟结果影响显著,其次为初始含水量和凋萎湿度,再次为粉粒含量、砂粒含量和土壤反射率;作物参数中的收获指数、光能利用率、热量单元指数、叶面积增长期占生长期的比例,对模拟结果影响显著,其次为作物生长最适温度、消光系数、作物生长下限温度、最大根深、最大叶面积指数、群体动态参数,再次为光能利用降低参数、叶面积指数动态曲线参数、叶面积指数衰减速率。     

A Varying Coefficients Model For Estimating Finite Population Totals: A Hierarchical Bayesian Approach

In some finite sampling situations, there is a primary variable that is sampled, and there are measurements on covariates for the entire population. A Bayesian hierarchical model for estimating totals for finite populations is proposed. A nonparametric linear model is assumed to explain the relationship between the dependent variable of interest and covariates. The regression coefficients in the linear model are allowed to vary as a function of a subset of covariates nonparametrically based on B-splines. The generality of this approach makes it robust and applicable to data collected using a variety of sampling techniques, provided the sample is representative of the finite population. A simulation study is carried out to evaluate the performance of the proposed model for the estimation of the population total. Results indicate accurate estimation of population totals using the approach. The modeling approach is used to estimate the total production of avocado for a large group of groves in Mexico.     

红枣提汁浓度随时间变化的数学模型

对红枣提汁浓度与浸提时间的关系,通过试验采集散点数据,并描绘散点图,建立数学模型,确认为双曲线数学模型。通过F检验与拟合检验,得知:浸提时间对可溶性固形物提取量的影响非常显著,回归方程拟合良好,可信度均在99％以上。该数学模型可为生产提供经济效益最高的浸提时间和最大的可溶性固形物的提取量。     

利用人工神经网络预报不同水分条件下作物根系发育参数

通过对人工神经网络理论的分析,建立了一个能够描述作物根——冠间非线性变化的模拟模型,利用植物地上部参数推求不同水分环境影响的地下根系参数。并通过改进BP算法解决了全局寻优的问题。利用精密的管栽试验为模型提供了足够的学习样本和检验样本。结果表明,该文建立的人工神经网络模型对描述根、冠间复杂的非线性关系方面具有相当高的精度和应用价值     

Insights Into the Latent Multinomial Model Through Mark-Resight Data on Female Grizzly Bears With Cubs-of-the-Year

Mark-resight designs for estimation of population abundance are common and attractive to researchers. However, inference from such designs is very limited when faced with sparse data, either from a low number of marked animals, a low probability of detection, or both. In the Greater Yellowstone Ecosystem, yearly mark-resight data are collected for female grizzly bears with cubs-of-the-year (FCOY), and inference suffers from both limitations. To overcome difficulties due to sparseness, we assume homogeneity in sighting probabilities over 16 years of bi-annual aerial surveys. We model counts of marked and unmarked animals as multinomial random variables, using the capture frequencies of marked animals for inference about the latent multinomial frequencies for unmarked animals. We discuss undesirable behavior of the commonly used discrete uniform prior distribution on the population size parameter and provide OpenBUGS code for fitting such models. The application provides valuable insights into subtleties of implementing Bayesian inference for latent multinomial models. We tie the discussion to our application, though the insights are broadly useful for applications of the latent multinomial model.