Bayesian modelling of environmental risk: example using a small area ecological study of coronary heart disease mortality in relation to modelled outdoor nitrogen oxide levels

Bayesian modelling of health risks in relation to environmental exposures offers advantages over conventional (non-Bayesian) modelling approaches. We report an example using research into whether, after controlling for different confounders, air pollution (NO_x) has a significant effect on coronary heart disease mortality, estimating the relative risk associated with different levels of exposure. We use small area data from Sheffield, England and describe how the data were assembled. We compare the results obtained using a generalized (Poisson) log-linear model with adjustment for overdispersion, with the results obtained using a hierarchical (Poisson) log-linear model with spatial random effects. Both classes of models were fitted using a Bayesian approach. Including spatial random effects models both overdispersion and spatial autocorrelation effects arising as a result of analysing data from small contiguous areas. The first modelling framework has been widely used, while the second provides a more rigorous model for hypothesis testing and risk estimation when data refer to small areas. When the models are fitted controlling only for the age and sex of the populations, the generalized log-linear model shows NO_x effects are significant at all levels, whereas the hierarchical log-linear model with spatial random effects shows significant effects only at higher levels. We then adjust for deprivation and smoking prevalence. Uncertainty in the estimates of smoking prevalence, arising because the data are based on samples, was accounted for through errors-in-variables modelling. NO_x effects apparently are significant at the two highest levels according to both modelling frameworks.

利用3种贝叶斯模型研究鱼类空间分布的影响因素以海州湾六丝钝尾虾虎鱼为例

栖息环境是生物生存的必要条件,生物与非生物因子共同影响海洋生物的空间分布。本研究以海州湾的六丝钝尾虾虎鱼（Amblychaeturichthys hexanema）为例,利用3种贝叶斯模型对2013−2022年春、秋季在海州湾进行的渔业资源底拖网调查和环境监测数据进行分析,探究六丝钝尾虾虎鱼的栖息分布特征以及主要影响因子。通过比较发现,贝叶斯正则化神经网络（BRNN）模型具有较好的拟合效果和预测性能,故本研究应用该模型进行分析。研究结果显示,六丝钝尾虾虎鱼的相对资源密度与饵料生物相对资源密度呈正相关关系;随着底层水温、底层盐度、水深、捕食者和竞争者的增加,六丝钝尾虾虎鱼的相对资源密度呈现先上升或保持相对平稳,而后下降的趋势。海州湾春、秋季六丝钝尾虾虎鱼的相对资源密度均呈现自西南向东北递减的趋势,且西南近岸浅海区的资源密度较高。秋季的资源密度高于春季,同时2018年、2021年和2022年秋季六丝钝尾虾虎鱼在34.7°～36°N、121°～121.6°E之间离岸较远的海域出现了资源聚集区。本研究将有助于深入了解六丝钝尾虾虎鱼的栖息分布特征及主要影响因素,为其资源养护和科学管理提供理论依据。     

Detection of changes in precipitation and runoff over eastern Canada and U.S. using a Bayesian approach

Inference about the existence and characteristics of changes in mean level of hydrometeorological sequences that may be generated by climatic variability is an important step before developing management rules in water resources systems. This paper presents a Bayesian approach, based on a single shifting model, which can be used to study a change in the mean level of a set of independent normal random variables. Two different problems are considered: the first is the detection of a change, while the second is the estimation of the change-point and its amplitude under the assumption that a change has occurred. This method is applied to precipitation and runoff data series over eastern Canada and U.S. during the twentieth century. The main results show an increase in the late sixties in the Eastern North American precipitation. This supports conclusions drawn from a number of studies which identified the late sixties to early seventies as a period of possible change.     

土地利用变化预测的案例推理方法

当前,基于案例的推理(Case-Based Reasoning,CBR)在解决复杂的地学问题时.对地学案例的表达和历史案例的相似性计算与推理存在明显缺陷,需要在CBR的表达模型和空间相似性计算与推理算法进行拓展.本文针对土地利用变化问题,首先在分析土地利用变化各种定量方法基础上,提出利用CBR进行土地利用变化分析的研究思路:其次,针对土地利用变化的空间特性及隐含的空间关系特性.给出土地利用变化案例的表达模型,案例间内蕴空间关系抽取算法,以及考虑案例间空间关系的CBR相似性推理模型:最后,进行珠江口区域土地利用变化的CBR方法试验.预测精度达到80%.为了进一步评价CBR方法对土地利用变化预测的有效性.在实例部分采用同样的实验数据进行贝叶斯网络的预测方法实验.由两种方法对比可知.CBR是从复杂到简单进行地学问题求解的一种有效方法.     

Development and Implementation of a Bayesian-based Aquifer Vulnerability Assessment in Florida

The Florida Aquifer Vulnerability Assessment (FAVA) was designed to provide a tool for environmental, regulatory, resource management, and planning professionals to facilitate protection of groundwater resources from surface sources of contamination. The FAVA project implements weights-of-evidence (WofE), a data-driven, Bayesian-probabilistic model to generate a series of maps reflecting relative aquifer vulnerability of Florida’s principal aquifer systems. The vulnerability assessment process, from project design to map implementation is described herein in reference to the Floridan aquifer system (FAS). The WofE model calculates weighted relationships between hydrogeologic data layers that influence aquifer vulnerability and ambient groundwater parameters in wells that reflect relative degrees of vulnerability. Statewide model input data layers (evidential themes) include soil hydraulic conductivity, density of karst features, thickness of aquifer confinement, and hydraulic head difference between the FAS and the watertable. Wells with median dissolved nitrogen concentrations exceeding statistically established thresholds serve as training points in the WofE model. The resulting vulnerability map (response theme) reflects classified posterior probabilities based on spatial relationships between the evidential themes and training points. The response theme is subjected to extensive sensitivity and validation testing. Among the model validation techniques is calculation of a response theme based on a different water-quality indicator of relative recharge or vulnerability: dissolved oxygen. Successful implementation of the FAVA maps was facilitated by the overall project design, which included a needs assessment and iterative technical advisory committee input and review. Ongoing programs to protect Florida’s springsheds have led to development of larger-scale WofE-based vulnerability assessments. Additional applications of the maps include land-use planning amendments and prioritization of land purchases to protect groundwater resources.     

Bayesian正则化BP神经网络拟合两类似大地水准面

为限制重力似大地水准面拟合到GPS/水准似大地水准面上的模型代表性误差,提出了Bayesian正则化BP神经网络拟合两类似大地水准面的新方法。利用某区域的重力似大地水准面模型和GPS/水准数据,将新方法与传统的曲面拟合法进行比较。在较大区域和两类似大地水准面差别不规则的情况下,Bayes-ian正则化BP神经网络有效地减少了拟合模型的代表性误差,而且通过Bayesian正则化算法对网络权值进行限制,抑制了过拟合现象。新方法提高了两面拟合结果的内、外符合精度。     

贝叶斯参数估计的最大熵方法的逆问题

讨论贝叶斯参数估计理论中利用最大熵原理确定参数的先验概率的逆问题,并且以泊松分布和指数分布为例给出证明.通过求解相应的微分方程和变分方程,得到所需约束条件.     

Application of fuzzy clustering and fuzzy classification to evaluate the provenance of glacial till

To evaluate the provenance of glacial till, the trace element content of magnetite was used. Magnetite was present in all known rock types and all till samples in the area investigated. By using fuzzy-set theory it was possible to group samples of magnetite taken from bedrock into relatively homogeneous and geologically meaningful groups and also, by fuzzy classification, to relate the till samples to the rocks in such a way that the relative contribution of each rock type to the till is estimated. Each rock and till sample is assigned a membership value between 0 and 1 for each rock type. The membership values, for a certain rock type in the till, are then interpolated by kriging onto maps. Magnetites from skarns associated with sulfide ores especially are rather distinct, and so a map of such membership values for till unveils all known ore deposits some 1–5 km downstreamin the general direction of the ice flow. Other anomalies show up which cannot be related to hitherto known ores or mineralizations.     

Stochastic prediction in geomorphology using Bayesian inference models

Bayesian inference modeling may be applied to empirical stochastic prediction in geomorphology where outcomes of geomorphic processes can be expressed by probability density functions. Natural variations in process outputs are accommodated by the probability model. Uncertainty in the values of model parameters is reduced by considering statistically independent prior information on long-term, parameter behavior. Formal combination of model and parameter information yields a Bayesian probability distribution that accounts for parameter uncertainty, but not for model uncertainty or systematic error which is ignored herein. Prior information is determined by ordinary objective or subjective methods of geomorphic investigation. Examples involving simple stochastic models are given, as applied to the prediction of shifts in river courses, alpine rock avalanches, and fluctuating river bed levels. Bayesian inference models may be applied spatially and temporally as well as to functions of a random variable. They provide technically superior forecasts, for a given shortterm data set, to those of extrapolation or stochastic simulation models. In applications the contribution of the field geomorphologist is of fundamental quantitative importance.