Smoothing and high risk areas detection in space-time disease mapping: a comparison of P-splines,autoregressive, and moving average models

Recently, several models have been proposed for smoothing risks in disease mapping. These models consider different ways of introducing both spatial and temporal dependence as well as spatio-temporal interactions. In this work, a comparison among some autoregressive, moving average, and P-spline models is performed. Firstly, brain cancer mortality data are used to analyze the degree of smoothness introduced by these models. Secondly, two separate simulation studies (one model-based and the other model-free) are carried out to evaluate the model performance in terms of bias, variability, sensitivity, and specificity. We conclude that P-spline models seem to be a good alternative to autoregressive and moving average models when analyzing highly sparse disease mapping data.     

Fast ensemble smoothing

Smoothing is essential to many oceanographic, meteorological, and hydrological applications. There are two predominant classes of smoothing problems. The first is fixed-interval smoothing, where the objective is to estimate model states within a time interval using all available observations in the interval. The second is fixed-lag smoothing, where the objective is to sequentially estimate model states over a fixed or indefinitely growing interval by restricting the influence of observations within a fixed window of time ahead of the evolving estimation time. In this paper, we use an ensemble-based approach to fixed-interval and fixed-lag smoothing, and synthesize two algorithms. The first algorithm is a fixed-interval smoother whose computation time is linear in the interval. The second algorithm is a fixed-lag smoother whose computation time is independent of the lag length. The complexity of these algorithms is presented, shown to improve upon existing implementations and verified with identical-twin experiments conducted with the Lorenz-95 system. Results suggest that ensemble methods yield efficient fixed-interval and fixed-lag smoothing solutions in the sense that the additional increment for smoothing is a small fraction of either filtering or model propagation costs in a practical ensemble application. We also show that fixed-interval smoothing can perform as fast as fixed-lag smoothing, and it may not be necessary to use a fixed-lag approximation for computational savings alone.     

射线类偏移成像中的模型平滑处理研究

本文从能量泛函的角度着手,基于速度梯度,采用最速下降法推导了基于偏微分方程的速度模型平滑公式,用于解决射线类偏移成像过程当中速度模型的平滑处理问题.同时针对偏微分方程速度模型平滑系数中阈值k的选取对速度模型空间结构的影响,在简单的高速体速度模型上分析了不同k值的选取对原始速度模型空间结构的改变,并通过射线路径和时间场的对比分析证明偏微分方程速度模型平滑处理相对于卷积算子平滑的优越性.最后通过在Marmousi、Sigsbee2A原始速度模型以及平滑处理后的速度模型上的成像结果分析验证偏微分方程模型平滑的有效性.     

The implementation of Bayesian structural additive regression models in multi-city time series air pollution and human health studies

In this study, a novel Bayesian semiparametric structural additive regression (STAR) model is introduced in multi-city time series air pollution and human health studies. This modeling approach can simultaneously take into account the fixed effects, random effects, nonlinear smoothing functions and spatial functions in an integrated model framework. This study focuses on examining the powerful functionalities of this approach in modeling air pollution and mortality data of 100 U.S. cities from 1987 to 2000. Compared with previous studies, the modeling approach used in this study yields consistent findings of nation-level and city-level PM₁₀ (particulate matter less than 10?μm) effects on mortality. Notably, cities with significantly elevated mortality rates were concentrated in the Northeastern U.S. This modeling approach also emphasizes the important functionality of the spatial function in visualizing disease mapping. Model diagnostics were performed to confirm the availability of the STAR model. We also found consistent findings by using different hyperparameters in the sensitivity analysis. To sum up, the implementation of this modeling approach has achieved the goals of applying a spatial function and obtaining robust results in the multi-city time series air pollution and human health study.     

空间光滑地震活动性模型中光滑函数的比较研究

使用Frankel提出的基于空间光滑地震活动性模型的地震危险性分析方法,选择华南、华北、川滇3个地区的地震记录,比较分析了高斯、幂律和地震分形分布光滑函数3种光滑函数在不同地区的适用性．结果表明,使用交叉验证法可以为高斯光滑函数选取合适的相关距离c值,光滑得到的地震活动性模型能够真实反映研究区域的地震活动特征,根据活动性模型计算得出的峰值加速度(PGA)分布也符合人们对研究区域地震危险性的认识．幂律光滑函数适用于地震活动性较强的地区,且具有容易求取光滑参数的优点．光滑程度较低的幂律光滑函数不适用于地震活动性弱的地区,在该类地区应选择光滑程度较高的高斯光滑函数．地震分形分布光滑函数不适用于地震活动较强且地震活动强度差异较大的地区,其容易过分高估高震级地震对地震危险性的影响,而忽略了低震级地震对地震危险性的贡献．但对于地震活动较弱且地震活动强度差异较小的地区,可使用地震分形分布光滑函数,且同样具有容易求取光滑参数的优点．      

Representing spatial dependence and spatial discontinuity in ecological epidemiology: a scale mixture approach

Variation in disease risk underlying observed disease counts is increasingly a focus for Bayesian spatial modelling, including applications in spatial data mining. Bayesian analysis of spatial data, whether for disease or other types of event, often employs a conditionally autoregressive prior, which can express spatial dependence commonly present in underlying risks or rates. Such conditionally autoregressive priors typically assume a normal density and uniform local smoothing for underlying risks. However, normality assumptions may be affected or distorted by heteroscedasticity or spatial outliers. It is also desirable that spatial disease models represent variation that is not attributable to spatial dependence. A spatial prior representing spatial heteroscedasticity within a model accommodating both spatial and non-spatial variation is therefore proposed. Illustrative applications are to human TB incidence. A simulation example is based on mainland US states, while a real data application considers TB incidence in 326 English local authorities.     

Determination of optimum kernel bandwidth for northern Marmara region,Turkey

As a relatively recent development, spatial smoothing methods have been introduced to identify seismic patterns. Among the methods developed to model the spatial variation, methods based on utilization of 3-D Gaussian isotropic kernels have a wide reception. The most important question remaining to be answered in the application of these methods is the determination of the optimum kernel bandwidth. At the present, researchers’ efforts to clarify the subject have still not yet finalized, this study aims to provide insightful knowledge for future efforts. In this study, for the region bounded by 27°–33° longitudes and 39°–41° latitudes, where the western section of the famous Northern Anatolian fault lies, smoothing techniques are implemented to determine the optimum smoothing kernel bandwidth for point sources. The influence of the modeling of seismicity through the computation of the optimum smoothing kernel bandwidth is examined. In addition, the sensitivity of each smoothing technique to the seismic patterns, whether densely clustered or scarcely populated, is investigated. In the end, the smoothing method based on optimum neighbor number is identified as highly sensitive to the density of seismicity and seismic clusters, and better in modeling high seismicity compared to the model based on single optimum smoothing distance used for the entire region of interest.     

基于偏微分方程的模型光滑处理在偏移成像中的应用

本文针对射线类偏移成像当中的速度模型光滑处理问题,借鉴数字图像处理当中的偏微分方程法,基于能量泛函,应用变分方法导出基于速度模型的偏微分方程实现射线类偏移成像当中的速度模型的光滑处理.由于偏微分方程法具有线性叠加特性、模型解的唯一性和局部特征保持性,因此,应用该算法可以实现基于原始速度模型空间结构的模型光滑处理.通过在原始速度模型以及光滑处理后的速度模型上计算速度的空间分布以及地震波走时、射线路径可以得出,偏微分方程法对速度模型的光滑处理能够很好地保持原始模型的空间结构,偏移成像结果也证明了该方法的实用性.     

Preserved travel‐time smoothing in orthorhombic media

Certain degree of smoothness of velocity models is required for most ray‐based migration and tomography. Applying conventional smoothing in model parameters results in offset‐dependent travel‐time errors for reflected events, which can be large even for small contrasts in model parameters between the layers. This causes the shift in both the depth and residual moveout of the migrated images. To overcome this problem in transversely isotropic medium with a vertical symmetry axis, the preserved travel‐time smoothing method was proposed earlier. We extend this method for orthorhombic media with and without azimuthal variation between the layers. We illustrate this method for a single interface between two orthorhombic layers and show that the smoothing‐driven errors in travel time are very small for practical application.     

华北地区中强地震发生时间的预测研究

通过对华北地区中强地震（指Ms≥5．5的地震）发生时间不均匀性的研究结果表明：自1815年以来，该区可划分为5个中强地震集中活跃时段。可用灰色系统理论和方法建立灰色预测模型。预测未来一个活跃时段的起止时间。如果发生在活跃时段内的中强地震的发生时间呈较好的线性趋势变化，则可用二指数平滑方法进行预测。在此基础上，本文还对它的预测精度作了估计。     

频率域波动方程正演基于多重网格预条件的迭代算法研究

频率域全波形反演是重要的地震成像方法,而频率域波动方程数值模拟是频率域全波形反演的基础.对于大规模的问题,由于受存储和计算量的限制,基于LU分解的直接方法一般不再适用,而是采用迭代方法.基于多重网格预条件的双共轭梯度稳定化方法是一种重要的迭代方法.本文重点讨论了多重网格预条件求解过程中的松弛因子选择方法,研究结果表明,(1)对于一般选取的松弛因子,随模型复杂性的增加,所能计算的重数逐渐下降,方法的实用性也随之下降;(2)对于复杂模型,采用局部模式分析方法选取松弛因子,提高了所能计算的重数,保证了多重网格方法的收敛性和实用性.这些研究成果对基于多重网格预条件的迭代算法的实际应用具有重要意义.     

地震层析成像LSQR算法的并行化

讨论了地震层析成像的LSQR算法(最小二乘QR分解). 在建立偏导数矩阵方程组时,对区内地震在方程中保留震源项,引入正交投影算子进行参数分离,对区外远震采用传统的平滑处理方式,用LSQR法求解联立的方程组. 由于区内地震的正交分解处理和区外远震的平滑处理,使得偏导数矩阵中的非零元素成倍增加,对于大型反演问题,这些非零元素常常达到几十GB到几百GB的数量级,巨量的内存占用成为LSQR算法的瓶颈. 针对这一问题,本文研究了偏导数矩阵中非零元素的分布规律,设计出合理的存储结构,采用分布式存储进行矩阵计算,提出了LSQR算法的并行化方案,并在联想深腾6800超级计算机上实现. 导出了LSQR算法的并行效率估算公式. 对两个地区的实际地震层析成像数据进行了效率测试.     

Regression Derivatives and Their Application to the Study of Geomagnetic Jerks

Geomagnetism and Aeronomy - New mathematical constructions are developed for the regression smoothing of discrete time series defined on an irregular grid. The new method is used to study secular...     

Localized identification of MDOF structures in the frequency domain

For the identification of multi-degree-of-freedom structures, it is not practical to identify all of the parameters included in the structures because enormous computation time is required and because identifiability may not be possible. In this paper, a localized identification approach through substructuring is formulated in the frequency domain. A technique of spectral smoothing is incorporated in the approach to deal with noise-corrupted data. The proposed approach can be used to identify the structural parameters in any part of interest in a structure. The numerical investigations for a lumped mass-spring-dashpot system indicate that faster convergence and higher accuracy are achieved and the noise influences on the identified results are reduced greatly by spectral smoothing. The approach also applies to whole-structure identification if the required records available and the numerical example shows that higher accuracy results are obtained with less cpu time and more poorly guessed initial values as compared with the general complete-structure identification.     

速度光滑对反射地震信号的影响分析

光滑处理使得单界面成为非均匀薄层,界面反射转变为层反射.为了探讨光滑处理的影响,以平面波作为入射波场,首先利用过渡层反射系数推导了反射信号的理论公式,然后就非均匀薄层下反射系数的计算问题,给出了具体的实现算法,并通过与经典Epstein过渡层反射系数解析结果的对比说明了算法的精度.最后在单界面及其被光滑后界面的对比分析中,得出了几点重要结论：随着光滑次数的增加,反射信号的到时基本保持不变,而反射信号的主频与能量呈减少趋势,其中信号能量在低光滑次数的衰减速率明显大于高光滑次数.     

ASSESSMENT OF MACCORMACK SCHEME IN UNSTEADY SEDIMENT LADEN FLOW COMPUTATION

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A traveling epidemic model of space–time disease spread

This work presents a random field model of disease attribute (incidence, mortality etc.) that transfers the study of the attribute distribution from the original spatiotemporal domain onto a lower-dimensionality traveling domain that moves along the direction of disease velocity. The partial differential equations connecting the disease attribute covariances in the original and the traveling domain are derived with coefficients that are functions of the disease velocity. These equations offer epidemiologic insight concerning the strength of the space–time dependence between the disease attribute values in the two domains. The traveling disease model has certain theoretical and computational advantages in the study and prediction of space–time disease attribute distributions in conditions of uncertainty. Estimates of the disease attribute are derived in the traveling domain and then used to generate maps of space–time disease attribute distribution in the original domain. The theoretical model is illustrated and additional insight is gained by means of a numerical mortality simulation study, which shows that the proposed model is at least as accurate but computationally more efficient than mainstream mapping techniques of higher dimensionality. These findings concerning the very good predictability of the proposed model also strongly support its adequacy to represent the space–time mortality distribution.     

Image-guided inversion in steady-state hydraulic tomography

In steady-state hydraulic tomography, the head data recorded during a series of pumping or/and injection tests can be inverted to determine the transmissivity distributions of an aquifer. This inverse problem is usually under-determined and ill-posed. We propose to use structural information inferred from a guiding image to constrain the inversion process. The guiding image can be drawn from soft data sets such as seismic and ground penetrating radar sections or from geological cross-sections inferred from the wells and some geological expertise. The structural information is extracted from the guiding image through some digital image analysis techniques. Then, it is introduced into the inversion process of the head data as a weighted four direction smoothing matrix used in the regularizer. Such smoothing matrix allows applying the smoothing along the structural features. This helps preserving eventual drops in the hydraulic properties. In addition, we apply a procedure called image-guided interpolation. This technique starts with the tomogram obtained from the image-guided inversion and focus this tomogram. These new approaches are applied on four synthetic toy problems. The hydraulic distributions estimated from the image-guided inversion are closer to the true transmissivity model and have higher resolution than those computed from a classical Gauss–Newton method with uniform isotropic smoothing.     

Effects of terrain smoothing on topographic shielding correction factors for cosmogenic nuclide‐derived estimates of basin‐averaged denudation rates

Estimation of spatially averaged denudation rates from cosmogenic nuclide concentrations in sediments depends on the surface production rates, the scaling methods of cosmic ray intensities, and the correction algorithms for skyline, snow and vegetation shielding used to calculate terrestrial cosmogenic nuclide production. While the calculation of surface nuclide production and application of latitude, altitude and palaeointensity scaling algorithms are subjects of active research, the importance of additional correction for shielding by topographic obstructions, snow and vegetation is the subject of ongoing debate. The derivation of an additional correction factor for skyline shielding for large areas is still problematic. One important issue that has yet to be addressed is the effect of the accuracy and resolution of terrain representation by a digital elevation model (DEM) on topographic shielding correction factors. Topographic metrics scale with the resolution of the elevation data, and terrain smoothing has a potentially large effect on the correction of terrestrial cosmogenic nuclide production rates for skyline shielding. For rough, high‐relief landscapes, the effect of terrain smoothing can easily exceed analytical errors, and should be taken into account. Here we demonstrate the effect of terrain smoothing on topographic shielding correction factors for various topographic settings, and introduce an empirical model for the estimation of topographic shielding factors based on landscape metrics. Copyright © 2008 John Wiley and Sons, Ltd.     

强震动记录H/V谱比法计算处理的若干关键环节

强震动记录H/V谱比法自提出以来,已广泛应用于地震工程各研究领域中。但对数据处理的2个关键环节——Taper预处理及傅氏谱平滑未有详细研究。因此,本文针对强震动记录H/V谱比法计算涉及的重要数据处理过程,对四川地区19个强震动台站在汶川地震余震中获取的642组强震动记录开展研究。研究实例表明:S波H/V谱比振幅在周期 < 1s时高于全时程,论证计算H/V谱比时截取S波窗口的必要性;S波窗口的截断会引起傅里叶振幅谱的边瓣效应,若不加以处理,将显著影响低频部分H/V谱比结果,Taper预处理对于消除这种截断误差具有良好效果;在兼顾平滑效果及卓越周期识别准确度的基础上,通过不同带宽的Parzen窗试算,认为0.5Hz带宽宜用于傅里叶H/V谱比曲线平滑。