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.

基于线性回归分析的主余震相关关系

预防强震后可能发生的余震对于保护灾区安全具有重要意义。为了对余震进行一定误差水平的快速判定,对主震与余震之间的关系进行分析。选取1970年1月1日—2009年9月30日全球范围5—10级地震进行预处理,采用基于最小二乘法的线性回归方法,对主震震级与最大余震震级关联关系、主震视应力与最大余震震级关联关系进行分析,并进行结果可视化。结果表明,主震与最大余震的震级存在一定线性关系,可为主震后在一定范围内对最大余震的快速判定提供一定参考。     

Ricker子波核最小二乘支持向量回归滤波方法的稳健性研究

除了信噪比、有效子波畸变等,稳健性(Robustness)也是度量滤波方法效果的一个重要的物理量,它刻画了滤波系统应对异常点值的能力.一般用影响函数作为评价稳健性的工具.支持向量机方法已较成功地应用于信号与图像的滤波中,尤其Ricker子波核方法更适于地震勘探信号处理.通过考察Ricker子波核最小二乘支持向量回归(LS-SVR:least squares support vector regression)滤波方法的影响函数,可以证明该方法的稳健性较差,本文用加权方法改善该方法的稳健性.经过大量理论实验得到一种改进的权函数,使加权之后的方法具有比较理想的稳健性.进一步用这个权函数辅助的加权Ricker子波LS-SVR处理含噪的合成与实际地震记录,都得到较好的效果.由具有平方损失函数的LS-SVR信号处理系统的无界影响函数出发,本文所提出的权函数可以有效地应用于具有相似损失函数的处理过程,如消噪、信号检测、提高分辨率与预测等问题.     

小波分析在地震资料去噪中的应用

本文阐述了小波变换和去噪的基本原理,根据模拟信号和实际地震信号的频谱分析,讨论了如何选择小波基,及去噪中的阈值问题,从小波分解出发,利用多尺度分解对地震资进行分析,并基于MATLAB语言和小波工具箱,实现了对地震资料的去噪.     

基于GRAIL重力数据的月球深部断裂识别和空间分布研究

月球深部断裂是研究月球早期应力场演化和动力机制的一类重要构造.本文基于GRAIL月球重力数据计算了全月布格重力梯度,在此基础上对月球深部断裂进行了全球绘制,共识别月球深部断裂226条.计算了断裂的长度和走向等基本参数,断裂总长度达到37137 km,平均长度为164 km.统计月球深部断裂在不同范围内的分布情况,发现多数断裂分布在月球的中低纬度地区,且北半球的断裂多于南半球.此外,大型月海集中区所在的纬向带断裂分布最多,断裂经向分布最多的区域为风暴洋的西侧.从全球尺度和不同经纬度带绘制断裂走向玫瑰花图,总体上月球全球尺度上的深部断裂表现出NE-SW和NW-SE的优势走向,不同经度带断裂的优势走向变化不明显,但在纬度带上有显著的变化.南北半球的中纬度带和高纬度带具有相同的优势走向,分别为NE-SW和NW-SE、E-W,在低纬度带的优势走向有所差异,分别是南半球的NE-SW和NW-SE以及北半球的N-S.

     

Application of wavelet analysis to crustal deformation data processing

Introduction The study mainly focused on tidal information, i.e. earth tide in the continuous deformationdata processing and analysis before. And the analysis methods used were specially for earth tideonly. As to the medium-long period and non-tidal information, fitting and filtering are not the bestmethods. Because they are not able to reflect the variation process of frequency information withtime and to distinguish and extract more earthquake information, although they can eliminateyea…     

Application of wavelet analysis to crustal deformation data processing

The time-frequency analysis and anomaly detection of wavelet transformation make the method irresistibly advantageous in non-stable signal processing. In the paper, the two characteristics are analyzed and demonstrated with synthetic signal. By applying wavelet transformation to deformation data processing, we find that about 4 months before strong earthquakes, several deformation stations near the epicenter received at the same time the abnormal signal with the same frequency and the period from several days to more than ten days. The GPS observation stations near the epicenter all received the abnormal signal whose period is from 3 months to half a year. These abnormal signals are possibly earthquake precursors. Foundation item: Joint Seismological Science Foundation of China (604021) and National Natural Science Foundation of China (40074024).     

Suspended load estimation using L1-fuzzy regression,L2-fuzzy regression and MARS-fuzzy regression models

ABSTRACT

The problem of estimation of suspended load carried by a river is an important topic for many water resources projects. Conventional estimation methods are based on the assumption of exact observations. In practice, however, a major source of natural uncertainty is due to imprecise measurements and/or imprecise relationships between variables. In this paper, using the Multivariate Adaptive Regression Splines (MARS) technique, a novel fuzzy regression model for imprecise response and crisp explanatory variables is presented. The investigated fuzzy regression model is applied to forecast suspended load by discharge based on two real-world datasets. The accuracy of the proposed method is compared with two well-known parametric fuzzy regression models, namely, the fuzzy least-absolutes model and the fuzzy least-squares model. The comparison results reveal that the MARS-fuzzy regression model performs better than the other models in suspended load estimation for the particular datasets. This comparison is done based on four goodness-of-fit criteria: the criterion based on similarity measure, the criterion based on absolute errors and the two objective functions of the fuzzy least-absolutes model and the fuzzy least-squares model. The proposed model is general and can be used for modelling natural phenomena whose available observations are reported as imprecise rather than crisp.

Editor D. Koutsoyiannis; Associate editor H. Aksoy     

利用多分辨率小波网络方法进行伪井反演

利用小波网络,对地震资料和小波多尺度分解属性资料,进行了虚井声波时差反演.讨论了利用地震信号的小波分解和网络学习、训练的理论方法.为了提高反演分辨率和精度，研究了信号分段相似小波时—频分析技术方法.在对对这些技术方法综合研究和算法的实现设计以后，对实际资料进行了反演计算，并对反演结果进行验证.取得了很好的效果.     

基于空间子集的地震数据分析方法(英文)

野外空间采样密度的提高将增加室内数据分析的工作量,常规的基于地震数据的点与线分析方法有一定的局限性。本文简要说明空间子集的抽取方法,列举了正交子集和斜交子集的特点,并通过三维可视化展示了子集数据的空间特性。提出在数据处理中利用子集的时间切片：（1）分析地震道空间分布的均匀性和规则性;（2）研究面波及规则干扰的空间分布特点;（3）检测叠前数据中的异常信息;（4）监控叠前去噪的效果。实际数据的应用结果表明基于空间子集的分析方法是一种独特有效的地震数据分析方法,从另一种视角观察地震数据,可以发现其中某些新的特征,以提高处理人员对数据的洞察能力。     

Evaluation of multiple regression models using spatial variables to predict nitrate concentrations in volcanic aquifers

Multiple linear regression of spatial variables including land use, soil type, and topography was applied to predict nitrate concentration and evaluate major factors affecting nitrate occurrence in springs and wells in the southern and northern areas of Jeju volcanic island, Korea. Three types of contributing area surrogates (CAS), namely circle, semicircle, and wedge, were employed to calculate the spatial variables. The regression results showed R² of 0.81–0.84 for springs and 0.74–0.77 for wells; R² values for wedge and semicircular CAS were more than 10% higher than those for circular CAS. The R² of spring models was significantly affected by both the shape and size of CAS, with optimal radii of 150–250 m and 300–400 m in the southern and northern areas, respectively, corresponding to thinner upper basaltic aquifers, and implying shorter flow paths in the southern area. The most influential variables in springs were orchards and soil types related to agriculture including silty loam and silty clay loam, indicating that nitrate levels are strongly affected by N fertilization in cultivated areas. In contrast, wells showed much less sensitivity to both shapes and sizes of CAS, with less contribution of land use and soil type to the regression, which could be attributed to a mix of multiple aquifer zones and widely different factors in the installation and operation of wells. Field parameters of electrical conductivity (EC) and pH increased the R² up to 10%, suggesting that these can be useful when regression with spatial variables yields a lower R². The optimal spatial scales for prediction of nitrate concentration and spatial variables that significantly contribute to nitrate contamination can provide relevant criteria for establishing groundwater management policies, considering the increasing anthropogenic land‐use trends on the island, where groundwater is highly sensitive to changes in spatial variables. Copyright © 2015 John Wiley & Sons, Ltd.     

Water temperature modelling: comparison between the generalized additive model,logistic, residuals regression and linear regression models

Water temperature has a significant influence on aquatic organisms, including stenotherm fish such as salmonids. It is thus of prime importance to build reliable tools to forecast water temperature. This study evaluated a statistical scheme to model average water temperature based on daily average air temperature and average discharge at the Sainte-Marguerite River, Northern Canada. The aim was to test a non-parametric water temperature generalized additive model (GAM) and to compare its performance to three previously developed approaches: the logistic, residuals regression and linear regression models. Due to its flexibility, the GAM was able to capture some of the nonlinear response between water temperature and the two explanatory variables (air temperature and flow). The shape of these effects was determined by the trends shown in the collected data. The four models were evaluated annually using a cross-validation technique. Three comparison criteria were calculated: the root mean square error (RMSE), the bias error and the Nash-Sutcliffe coefficient of efficiency (NSC). The goodness of fit of the four models was also compared graphically. The GAM was the best among the four models (RMSE = 1.44°C, bias = ?0.04 and NSC = 0.94).     

Stochastic analysis of spatiotemporal solute content measurements using a regression model

A regression model is used to study spatiotemporal distributions of solute content ion concentration data (calcium, chloride and nitrate), which provide important water contamination indicators. The model consists of three random and one deterministic components. The random space/time component is assumed to be homogeneous/stationary and to have a separable covariance. The purely spatial and the purely temporal random components are assumed to have homogenous and stationary increments, respectively. The deterministic component represents the space/time mean function. Inferences of the random components involve maximum likelihood and semi-parametric methods under some restrictions on the data configuration. Computational advantages and modelling limitations of the assumptions underlying the regression model are discussed. The regression model leads to simplifications in the space/time kriging and cokriging systems used to obtain space/time estimates at unobservable locations/instants. The application of the regression model in the study of the solute content ions was done at a global scale that covers the entire region of interest. The variability analysis focuses on the calculation of the spatial direct and cross-variograms and the evaluation of correlations between the three solute content ions. The space/time kriging system is developed in terms of the space direct and cross-variograms, and allows the separate estimation of the regression model components. Maps of these components are then obtained for each one of the three ions. Using the estimates of the purely spatial component, spatial dependencies between the ions are studied. Physical causes and consequences of the space/time variability are discussed, and comparisons are made with previous analyses of the solute content dataset.     

Regional flood frequency analysis using Bayesian generalized least squares: a comparison between quantile and parameter regression techniques

Regression‐based regional flood frequency analysis (RFFA) methods are widely adopted in hydrology. This paper compares two regression‐based RFFA methods using a Bayesian generalized least squares (GLS) modelling framework; the two are quantile regression technique (QRT) and parameter regression technique (PRT). In this study, the QRT focuses on the development of prediction equations for a flood quantile in the range of 2 to 100 years average recurrence intervals (ARI), while the PRT develops prediction equations for the first three moments of the log Pearson Type 3 (LP3) distribution, which are the mean, standard deviation and skew of the logarithms of the annual maximum flows; these regional parameters are then used to fit the LP3 distribution to estimate the desired flood quantiles at a given site. It has been shown that using a method similar to stepwise regression and by employing a number of statistics such as the model error variance, average variance of prediction, Bayesian information criterion and Akaike information criterion, the best set of explanatory variables in the GLS regression can be identified. In this study, a range of statistics and diagnostic plots have been adopted to evaluate the regression models. The method has been applied to 53 catchments in Tasmania, Australia. It has been found that catchment area and design rainfall intensity are the most important explanatory variables in predicting flood quantiles using the QRT. For the PRT, a total of four explanatory variables were adopted for predicting the mean, standard deviation and skew. The developed regression models satisfy the underlying model assumptions quite well; of importance, no outlier sites are detected in the plots of the regression diagnostics of the adopted regression equations. Based on ‘one‐at‐a‐time cross validation’ and a number of evaluation statistics, it has been found that for Tasmania the QRT provides more accurate flood quantile estimates for the higher ARIs while the PRT provides relatively better estimates for the smaller ARIs. The RFFA techniques presented here can easily be adapted to other Australian states and countries to derive more accurate regional flood predictions. Copyright © 2011 John Wiley & Sons, Ltd.     

Modelling effects of spatial variability of saturated hydraulic conductivity on autocorrelated overland flow data: linear mixed model approach

The mixed linear model approach was introduced and applied in studying the effects of spatial variation of the saturated hydraulic conductivity (K _s ) on the variation of the overland flow. Analysis was carried out with 2,000 rainfall-runoff events, all generated through transformation of real, observed rainfall events and different spatially variable K _s fields in a small (12 ha) agricultural catchment. The parameters accounting for the variation in the generation method were the coefficient of variation (cv) and correlation length (L _x L _y ) of K _s both having two levels of values obtained from field measurements of other studies. The analysis showed that the combinations with both parameters having the smaller or bigger value during flow peaks only caused different response in the overland flow. However, the parameters were statistically significant only at the 10% level. Most of the flow variation was explained by the event dynamics. The mixed models were able to model the structure of the data efficiently with less restrictive assumptions than for example the analysis of variance, hence producing more reliable results. The method was able to take into account autocorrelation of the test series, correlation between the factors and unequal variances. The usefulness of the method was supported by the fact that the conclusions drawn by it were confirmed by simple, conventional methods of a previous study, added with statistical criteria and confidence levels for each calculation moment. The findings of the study can be utilized in practise for example when designing the field sampling experiments.     

Characteristics analysis on high density spatial sampling seismic data

China＇s continental deposition basins are characterized by complex geological structures and various reservoir lithologies. Therefore, high precision exploration methods are needed. High density spatial sampling is a new technology to increase the accuracy of seismic exploration. We briefly discuss point source and receiver technology, analyze the high density spatial sampling in situ method, introduce the symmetric sampling principles presented by Gijs J. O. Vermeer, and discuss high density spatial sampling technology from the point of view of wave field continuity. We emphasize the analysis of the high density spatial sampling characteristics, including the high density first break advantages for investigation of near surface structure, improving static correction precision, the use of dense receiver spacing at short offsets to increase the effective coverage at shallow depth, and the accuracy of reflection imaging. Coherent noise is not aliased and the noise analysis precision and suppression increases as a result. High density spatial sampling enhances wave field continuity and the accuracy of various mathematical transforms, which benefits wave field separation. Finally, we point out that the difficult part of high density spatial sampling technology is the data processing. More research needs to be done on the methods of analyzing and processing huge amounts of seismic data.     

高密度空间采样地震数据特点分析

中国陆相沉积盆地的地质结构复杂,储层岩性的多变,需要有高精度的勘探方法。高密度空间采样是提高地震勘探精度的一项新技术。本文简要说明了点激发和点接收技术,分析高密度空间采样的野外工作方法,介绍了Gijs j．o．Vermeer提出的对称采样原理,从波场连续性的角度探讨了高密度空间采样技术。重点分析高密度空间采样数据的特点, 即:高密集的初至波有利于近地表结构的调查,可提高静校正的精度;小偏移距、小点距接收增加了浅层的有效覆盖次数,提高浅层反射的成像精度; 对规则噪声可实现无假频采样,室内的噪声分析和噪声压制的精度随着提高;高密度采集使波场连续性增强,使得各种数学变换的精度提高,有利于不同波场的分离。最后指出高密度空间采样地震勘探技术的难点在于室内数据处理,针对海量数据的分析和处理方法还需要进行深入细致的研究工作。     

Assessing the relationships between elevation and extreme precipitation with various durations in southern Taiwan using spatial regression models

A spatially autocorrelated effect exists in precipitation of a mountainous basin. This study examines the relationship between maximum annual rainfall and elevation in the Kaoping River Basin of southern Taiwan using spatial regression models (i.e. geographically weighted regression (GWR), simultaneous autoregression (SAR), and conditional autoregression (CAR)). Results show that the GWR, SAR, and CAR models can improve spatial data fitting and provide an enhanced estimation for the rainfall–elevation relationship than the ordinary least squares approach. In particular, GWR achieves the most accurate estimation, and SAR and CAR achieve similar performance in terms of the Akaike information criterion. The relationship between extreme rainfall and elevation for longer duration is more concise than that for short durations. Results show that the spatial distribution of precipitation depends on elevation and that rainfall patterns in study area are heterogeneous between the southwestern plain and the eastern mountain area. Copyright © 2011 John Wiley & Sons, Ltd.     

Environmental and spatial patterns as drivers of littoral macroinvertebrate assemblages in patchily distributed mountain lakes: Contribution to typology design

Biological assemblages are affected by both environmental and spatial processes. Spatial autocorrelation can be specially marked in discrete ecosystems patchily distributed over a large region (e.g., lakes arranged in districts). Lake typologies are exclusively based on environmental features, but we hardly know to what extent spatial patterns can hinder their implementation. We analysed the role of environmental factors and spatial autocorrelation in shaping littoral macroinvertebrate communities of 51 mountain lakes from a large Spanish region in order to test: 1) the suitability of the variables currently used to construct typologies; 2) the influence of spatial patterns on typology implementation. Biologically meaningful types of lakes were created and described by means of cluster analysis (Jaccard index) and multiple discriminant analysis. Water permanence, substrate type and vegetation were the main drivers of the assemblage composition. The cluster analysis and Mantel tests showed that spatial patterns did not generally hamper recognizing lake types. Only in the district with lakes closest to each other (Sanabria Natural Park), spatial autocorrelation was strong enough to overcome the effects of some factors (substrate type), but not others (water permanence).