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1.
Several risk and decision analysis applications are characterized by spatial elements: there are spatially dependent uncertain variables of interest, decisions are made at spatial locations, and there are opportunities for spatial data acquisition. Spatial dependence implies that the data gathered at one coordinate could inform and assist a decision maker at other locations as well, and one should account for this learning effect when analyzing and comparing information gathering schemes. In this paper, we present concepts and methods for evaluating sequential information gathering schemes in spatial decision situations. Static and sequential information gathering schemes are outlined using the decision theoretic notion of value of information, and we use heuristics for approximating the value of sequential information in large-size spatial applications. We illustrate the concepts using a Bayesian network example motivated from risks associated with CO2 sequestration. We present a case study from mining where there are risks of rock hazard in the tunnels, and information about the spatial distribution of joints in the rocks may lead to a better allocation of resources for choosing rock reinforcement locations. In this application, the spatial variables are modeled by a Gaussian process. In both examples there can be large values associated with adaptive information gathering.  相似文献   

2.
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.  相似文献   

3.
Stochastic Environmental Research and Risk Assessment - Conditional autoregressive distributions are commonly used to model spatial dependence between nearby geographic units in disease mapping...  相似文献   

4.
In this paper we derive score tests for spatial independence in mortality or incidence risk in the framework of hierarchical spatial models where different Gaussian Markov random field (MRF) priors are given for modelling the area random effects (specifically, two non-intrinsic Gaussian priors and a convolution Gaussian prior). The techniques used to test the practically relevant and important simplifying hypotheses of an absence of spatial variation in risk will provide a guidance for practitioners to select an adequate model (i.e., a model with an exchangeable-independent-prior, an intrinsic prior, a convolution prior or a non-intrinsic prior, for the area-specific random effects distribution). The proposed methodology is illustrated by analyzing the well-known data set of lip cancer in Scotland and female mortality due to cerebrovascular disease in Navarra, Spain.  相似文献   

5.
Calibration of hydrologic models is very difficult because of measurement errors in input and response, errors in model structure, and the large number of non-identifiable parameters of distributed models. The difficulties even increase in arid regions with high seasonal variation of precipitation, where the modelled residuals often exhibit high heteroscedasticity and autocorrelation. On the other hand, support of water management by hydrologic models is important in arid regions, particularly if there is increasing water demand due to urbanization. The use and assessment of model results for this purpose require a careful calibration and uncertainty analysis. Extending earlier work in this field, we developed a procedure to overcome (i) the problem of non-identifiability of distributed parameters by introducing aggregate parameters and using Bayesian inference, (ii) the problem of heteroscedasticity of errors by combining a Box–Cox transformation of results and data with seasonally dependent error variances, (iii) the problems of autocorrelated errors, missing data and outlier omission with a continuous-time autoregressive error model, and (iv) the problem of the seasonal variation of error correlations with seasonally dependent characteristic correlation times. The technique was tested with the calibration of the hydrologic sub-model of the Soil and Water Assessment Tool (SWAT) in the Chaohe Basin in North China. The results demonstrated the good performance of this approach to uncertainty analysis, particularly with respect to the fulfilment of statistical assumptions of the error model. A comparison with an independent error model and with error models that only considered a subset of the suggested techniques clearly showed the superiority of the approach based on all the features (i)–(iv) mentioned above.  相似文献   

6.
The existence of time‐dependent variance or conditional variance, commonly called heteroscedasticity, in hydrologic time series has not been thoroughly investigated. This paper deals with modelling the heteroscedasticity in the residuals of the seasonal autoregressive integrated moving average (SARIMA) model using a generalized autoregressive conditional heteroscedasticity (GARCH) model. The model is applied to two monthly rainfall time series from humid and arid regions. The effect of Box–Cox transformation and seasonal differencing on the remaining seasonal heteroscedasticity in the residuals of the SARIMA model is also investigated. It is shown that the seasonal heteroscedasticity in the residuals of the SARIMA model can be removed using Box–Cox transformation along with seasonal differencing for the humid region rainfall. On the other hand, transformation and seasonal differencing could not remove heteroscedasticity from the residuals of the SARIMA model fitted to rainfall data in the arid region. Therefore, the GARCH modelling approach is necessary to capture the heteroscedasticity remaining in the residuals of a SARIMA model. However, the evaluation criteria do not necessarily show that the GARCH model improves the performance of the SARIMA model. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

7.
Multivariate time series modeling approaches are known as useful tools for describing, simulating, and forecasting hydrologic variables as well as their changes over the time. These approaches also have temporal and cross-sectional spatial dependence in multiple measurements. Although the application of multivariate linear and nonlinear time series approaches such as vector autoregressive with eXogenous variables (VARX) and multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) models are commonly used in financial and economic sciences, these approaches have not been extensively used in hydrology and water resources engineering. This study employed VARX and VARX–MGARCH approaches in modeling mean and conditional heteroscedasticity of daily rainfall and runoff records in the basin of Zarrineh Rood Dam, Iran. Bivariate diagonal VECH (DVECH) model, as a main type of MGARCH, shows how the conditional variance–covariance and conditional correlation structure vary over the time between residuals series of the fitted VARX. For this purpose, five model fits, which consider different combinations of twofold rainfall and runoff, including both upstream and downstream stations, have been investigated in the present study. The VARX model, with different orders, was applied to the daily rainfall–runoff process of the study area in each of these model fits. The Portmanteau test revealed the existence of conditional heteroscedasticity in the twofold residuals of fitted VARX models. Therefore, the VARX–DVECH model is proposed to capture the heteroscedasticity existing in the daily rainfall–runoff process. The bivariate DVECH model indicated both short-run and long-run persistency in the conditional variance–covariance matrix related to the twofold innovations of rainfall–runoff processes. Furthermore, the evaluation criteria for the VARX–DVECH model revealed the improvement of VARX model performance.  相似文献   

8.
A multivariate spatial sampling design that uses spatial vine copulas is presented that aims to simultaneously reduce the prediction uncertainty of multiple variables by selecting additional sampling locations based on the multivariate relationship between variables, the spatial configuration of existing locations and the values of the observations at those locations. Novel aspects of the methodology include the development of optimal designs that use spatial vine copulas to estimate prediction uncertainty and, additionally, use transformation methods for dimension reduction to model multivariate spatial dependence. Spatial vine copulas capture non-linear spatial dependence within variables, whilst a chained transformation that uses non-linear principal component analysis captures the non-linear multivariate dependence between variables. The proposed design methodology is applied to two environmental case studies. Performance of the proposed methodology is evaluated through partial redesigns of the original spatial designs. The first application is a soil contamination example that demonstrates the ability of the proposed methodology to address spatial non-linearity in the data. The second application is a forest biomass study that highlights the strength of the methodology in incorporating non-linear multivariate dependence into the design.  相似文献   

9.
Entropy-based correlated shrinkage of spatial random processes   总被引：1，自引：1，他引：0  
This paper proposes a two-stage correlated non-linear shrinkage estimation methodology for spatial random processes. A block hard thresholding design, based on Shannon’s entropy, is formulated in the first stage. The thresholding design is adaptive to each resolution level, because it depends on the empirical distribution function of the mutual information ratios between empirical wavelet blocks and the random variables of interest, at each scale. In the second stage, a global correlated (inter- and intra-scale) shrinkage is applied to approximate the values of interest of the underlying spatial process. Additionally, a simulation study is developed, in the Gaussian context, to analyze the sensitivity, measured by empirical stochastic ordering, of the entropy-based block hard thresholding stage in relation to the parameters characterizing local variability (fractality) and dependence range of the spatial process of interest, the noise level, and the design of the region of interest.  相似文献   

10.
Generation of replicates of the available data enables the researchers to solve different statistical problems, such as the estimation of standard errors, the inference of parameters or even the approximation of distribution functions. With this aim, Bootstrap approaches are suggested in the current work, specifically designed for their application to spatial data, as they take into account the dependence structure of the underlying random process. The key idea is to construct nonparametric distribution estimators, adapted to the spatial setting, which are distribution functions themselves, associated to discrete or continuous random variables. Then, the Bootstrap samples are obtained by drawing at random from the estimated distribution. Consistency of the suggested approaches will be proved by assuming stationarity from the random process or by relaxing the latter hypothesis to admit a deterministic trend. Numerical studies for simulated data and a real data set, obtained from environmental monitoring, are included to illustrate the application of the proposed Bootstrap methods.  相似文献   

11.
The spatial distribution of residual light non-aqueous phase liquid (LNAPL) is an important factor in reactive solute transport modeling studies. There is great uncertainty associated with both the areal limits of LNAPL source zones and smaller scale variability within the areal limits. A statistical approach is proposed to construct a probabilistic model for the spatial distribution of residual NAPL and it is applied to a site characterized by ultra-violet-induced-cone-penetration testing (CPT–UVIF). The uncertainty in areal limits is explicitly addressed by a novel distance function (DF) approach. In modeling the small-scale variability within the areal limits, the CPT–UVIF data are used as primary source of information, while soil texture and distance to water table are treated as secondary data. Two widely used geostatistical techniques are applied for the data integration, namely sequential indicator simulation with locally varying means (SIS–LVM) and Bayesian updating (BU). A close match between the calibrated uncertainty band (UB) and the target probabilities shows the performance of the proposed DF technique in characterization of uncertainty in the areal limits. A cross-validation study also shows that the integration of the secondary data sources substantially improves the prediction of contaminated and uncontaminated locations and that the SIS–LVM algorithm gives a more accurate prediction of residual NAPL contamination. The proposed DF approach is useful in modeling the areal limits of the non-stationary continuous or categorical random variables, and in providing a prior probability map for source zone sizes to be used in Monte Carlo simulations of contaminant transport or Monte Carlo type inverse modeling studies.  相似文献   

12.
Typhoon is one of the most destructive disasters in Taiwan, which usually causes many floods and mudslides and prevents the electrical and water supply. Prior to its arrival, how to accurately forecast the path and rainfall of typhoon are important issues. In the past, a regression-based model was the most applied statistical method to evaluate the associated problems. However, it generally ignored the spatial dependence in the data, resulting in less accurate estimation and prediction, and the importance of particular explanatory variables may not be apparent. Therefore, in this paper we focus on assessing the spatial risk variations regarding the typhoon cumulated rainfall at Taipei with respect to typhoon locations by using the spatial hierarchical Bayesian model combined with the spatial conditional autoregressive model, where the model parameters are estimated by designing a family of stochastic algorithms based on a Markov chain Monte Carlo technique. The proposed method is applied to a real data set of Taiwan for illustration. Also, some important explanatory variables regarding the typhoon cumulated rainfall at Taipei are indicated as well.  相似文献   

13.
This paper examines spatial variations of urban growth patterns in Chinese cities through a case study of Dongguan, a rapidly industrializing city characterized by a bottom-up pattern of development based on townships. We have employed both non-spatial and spatial logistic regression models to analyze urban land conversion. The non-spatial logistic regression has found the significance of accessibility, neighborhood conditions and socioeconomic factors for urban development. The logistic regression with spatially expanded coefficients significantly improves the orthodoxy logistic regression with lower levels of spatial autocorrelation of residuals and better goodness-of-fit. More importantly, the spatial logistic model reveals the spatially varying relationship between urban growth and its underlying factors, particularly the local influence of environment protection and urban development policies. The results of the spatial logistic model also provide clear clues for assessing environmental risks to take the local contexts into account.  相似文献   

14.
Long-term trends in the ocean wave climate because of global warming are of major concern to many stakeholders within the maritime industries, and there is a need to take severe sea state conditions into account in design of marine structures and in marine operations. Various stochastic models of significant wave height are reported in the literature, but most are based on point measurements without exploiting the flexible framework of Bayesian hierarchical space–time models. This framework allows modelling of complex dependence structures in space and time and incorporation of physical features and prior knowledge, yet remains intuitive and easily interpreted. This paper presents a Bayesian hierarchical space–time model with a log-transform for significant wave height data for an area in the North Atlantic ocean. The different components of the model will be outlined, and the results from applying the model to data of different temporal resolutions will be discussed. Different model alternatives have been tried and long-term trends in the data have been identified for all model alternatives. Overall, these trends are in reasonable agreement and also agree fairly well with previous studies. The log-transform was included in order to account for observed heteroscedasticity in the data, and results are compared to previous results where a similar model was employed without a log-transform. Furthermore, a discussion of possible extensions to the model, e.g. incorporating regression terms with relevant meteorological data, will be presented.  相似文献   

15.
The spatial variability of each parameter affecting storm runoff must be accounted for in distributed modelling. The objective of the work reported here is to assess the effects of using distributed versus lumped hydraulic roughness coefficients in the modelling of direct surface runoff. A spatially variable data set composed of Manning roughness coefficients is used to model direct surface runoff. To assess the information content (as measured by entropy) of spatially variable data and its significance in distributed modelling, various degrees of smoothing are applied. The error resulting from smoothing the hydraulic roughness coefficients is determined by modelling overland flow using a finite element solution. The Manning roughness coefficients were taken from field measurements of the Manning roughness coefficient at 0.6 m on a 14 m hillslope. These values were then used in a numerical simulation of outflow hydrographs to investigate the dependence of error on spatial variability. Our study focuses on the characteristics of spatial data used in distributed hydrological modelling. The field sites have fractal dimensions of ≈? 1.4, which is close to a Brownian variation. The sampling interval that captures the essential spatial variability of the Manning roughness coefficient does not seem to matter due to its Brownian variation in the field sites. Hence due to the nearly uniform random distribution, measurements at 0.6 m intervals are not necessary and larger intervals would yield results that are just as acceptable provided the mean value together with a uniformly random distribution is maintained for any size of finite element or sampling resolution. Because detailed measurements of hydraulic roughness are not practically available for deterministic catchment modelling, it is important to know that larger sampling resolutions may be used than 0.6 m.  相似文献   

16.
Due to the fast pace increasing availability and diversity of information sources in environmental sciences, there is a real need of sound statistical mapping techniques for using them jointly inside a unique theoretical framework. As these information sources may vary both with respect to their nature (continuous vs. categorical or qualitative), their spatial density as well as their intrinsic quality (soft vs. hard data), the design of such techniques is a challenging issue. In this paper, an efficient method for combining spatially non-exhaustive categorical and continuous data in a mapping context is proposed, based on the Bayesian maximum entropy paradigm. This approach relies first on the definition of a mixed random field, that can account for a stochastic link between categorical and continuous random fields through the use of a cross-covariance function. When incorporating general knowledge about the first- and second-order moments of these fields, it is shown that, under mild hypotheses, their joint distribution can be expressed as a mixture of conditional Gaussian prior distributions, with parameters estimation that can be obtained from entropy maximization. A posterior distribution that incorporates the various (soft or hard) continuous and categorical data at hand can then be obtained by a straightforward conditionalization step. The use and potential of the method is illustrated by the way of a simulated case study. A comparison with few common geostatistical methods in some limit cases also emphasizes their similarities and differences, both from the theoretical and practical viewpoints. As expected, adding categorical information may significantly improve the spatial prediction of a continuous variable, making this approach powerful and very promising.  相似文献   

17.
基于ARMA模型非因果空间预测滤波(英文)   总被引：3，自引：1，他引：2  
常规频域预测滤波方法是建立在自回归(autoregressive,AR)模型基础上的,这导致滤波过程中前后假设的不一致,即首先利用源噪声的假设计算误差剖面,却又将其作为可加噪声而从原始剖面中减去来得到有效信号。本文通过建立自回归-滑动平均(autoregres sive/moving-average,ARMA)模型,首先求解非因果预测误差滤波算子,然后利用自反褶积形式投影滤波过程估计可加噪声,进而达到去除随机噪声目的。此过程有效避免了基于AR模型产生的不一致性。在此基础上,将一维ARMA模型扩展到二维空间域,实现了基于二维ARMA模型频域非因果空间预测滤波在三维地震资料随机噪声衰减中的应用。模型试验与实际资料处理表明该方法在很好保留反射信息同时,压制随机噪声更加彻底,明显优于常规频域预测去噪方法。  相似文献   

18.
Bovine tuberculosis (TB) poses a serious threat for agricultural industry in several countries, it involves potential interactions between wildlife and cattle and creates societal problems in terms of human-wildlife conflict. This study addresses connectedness network analysis, the spatial, and temporal dynamics of TB between cattle in farms and the European badger (Meles meles) using a large dataset generated by a calibrated agent based model. Results showed that infected network connectedness was lower in badgers than in cattle. The contribution of an infected individual to the mean distance of disease spread over time was considerably lower for badger than cattle; badgers mainly spread the disease locally while cattle infected both locally and across longer distances. The majority of badger-induced infections occurred when individual badgers leave their home sett, and this was positively correlated with badger population growth rates. Point pattern analysis indicated aggregation in the spatial pattern of TB prevalence in badger setts across all scales. The spatial distribution of farms that were not TB free was aggregated at different scales than the spatial distribution of infected badgers and became random at larger scales. The spatial cross correlation between infected badger setts and infected farms revealed that generally infected setts and farms do not coexist except at few scales. Temporal autocorrelation detected a two year infection cycle for badgers, while there was both within the year and longer cycles for infected cattle. Temporal cross correlation indicated that infection cycles in badgers and cattle are negatively correlated. The implications of these results for understanding the dynamics of the disease are discussed.  相似文献   

19.
In the analysis of spatiotemporal processes underlying environmental studies, the estimation of the non-stationary spatial covariance structure is a well known issue in which multidimensional scaling (MDS) provides an important methodological approach (Sampson and Guttorp in J Am Stat Assoc 87:108–119, 1992). It is also well known that approximating dispersion by a non-metric MDS procedure offers, in general, low precision when accurate differences in spatial dispersion are needed for interpolation purposes, specially if a low dimensional configuration is employed besides a high number of stations in oversampled domains. This paper presents a modification, consisting of including geographical spatial constraints, of Heiser and Groenen’s (Psychometrika 62:63–83, 1997) cluster differences scaling algorithm by which not the original stations but the cluster centres can be represented, while the stations and clusters retain their spatial relationships. A decomposition of the sum of squared dissimilarities into contributions from several sources of variation can be employed for an exploratory diagnosis of the model. Real data are analyzed and differences between several cluster-MDS strategies are discussed.  相似文献   

20.
A scheme for meteorological drought analysis at various temporal and spatial scales based on a spatial Bayesian interpolation of drought severity derived from Standardized Precipitation Index (SPI) values at observed stations is presented and applied to the Huai River basin of China in this paper, using monthly precipitation record from 1961 to 2006 in 30 meteorological stations across the basin. After dividing the study area into regular grids, drought condition in gauged sites are classified into extreme, severe, moderate and non drought according to SPIs at month, seasonal and annual time scales respectively while that in ungauged grids are explained as risks of various drought severities instead of single state by a Bayesian interpolation. Subsequently, temporal and spatial patterns of drought risks are investigated statistically. Main conclusions of the research are as follows: (1) drought at seasonal scale was more threatening than the other two time scales with a larger number of observed drought events and more notable variation; (2) results of the Mann–Kendall test revealed an upward trend of drought risk in April and September; (3) there were larger risks of extreme and severe drought in southern and northwestern parts of the basin while the northeastern areas tended to face larger risks of moderate drought. The case study in Huai River basin suggests that the proposed approach is a viable and flexible tool for monitoring meteorological drought at multiple scales with a more specific insight into drought characteristics at each severity level.  相似文献   

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