共查询到20条相似文献，搜索用时 31 毫秒
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This paper investigates the effects of uncertainty in rock-physics models on reservoir parameter estimation using seismic amplitude variation with angle and controlled-source electromagnetics data. The reservoir parameters are related to electrical resistivity by the Poupon model and to elastic moduli and density by the Xu-White model. To handle uncertainty in the rock-physics models, we consider their outputs to be random functions with modes or means given by the predictions of those rock-physics models and we consider the parameters of the rock-physics models to be random variables defined by specified probability distributions. Using a Bayesian framework and Markov Chain Monte Carlo sampling methods, we are able to obtain estimates of reservoir parameters and information on the uncertainty in the estimation. The developed method is applied to a synthetic case study based on a layered reservoir model and the results show that uncertainty in both rock-physics models and in their parameters may have significant effects on reservoir parameter estimation. When the biases in rock-physics models and in their associated parameters are unknown, conventional joint inversion approaches, which consider rock-physics models as deterministic functions and the model parameters as fixed values, may produce misleading results. The developed stochastic method in this study provides an integrated approach for quantifying how uncertainty and biases in rock-physics models and in their associated parameters affect the estimates of reservoir parameters and therefore is a more robust method for reservoir parameter estimation. 相似文献
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Yun-Huan Lee Hong-Ding Yang Chun-Shu Chen 《Stochastic Environmental Research and Risk Assessment (SERRA)》2012,26(4):509-517
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
4.
The purpose of this article is to show how Bayesian belief networks can beused in analysis of the sequence of the earthquakes which have occurred in a region, to study the interaction among the variables characterizing eachevent. These relationships can be represented by means of graphs consistingof vertices and edges; the vertices correspond to random variables, whilethe edges express properties of conditional independence. We have examinedItalian seismicity as reported in two data bases, the NT4.1.1 catalogue and the ZS.4 zonation, and taken into account three variables: the size of thequake, the time elapsed since the previous event, and the time before the subsequent one. Assigning different independence relationships among these variables, first two couples of bivariate models, and then eight trivariatemodels have been defined. After presenting the main elements constituting a Bayesian belief network, we introduce the principal methodological aspects concerning estimation and model comparison. Following a fully Bayesian approach, prior distributions are assigned on both parameters and structuresby combining domain knowledge and available information on homogeneous seismogenic zones. Two case studies are used to illustrate in detail the procedure followed to evaluate the fitting of each model to the data sets andcompare the performance of alternative models. All eighty Italian seismogenic zones have been analysed in the same way; the results obtained are reportedbriefly. We also show how to account for model uncertainty in predicting a quantity of interest, such as the time of the next event. 相似文献
5.
An extended Bayesian sediment fingerprinting mixing model for the full Bayes treatment of geochemical uncertainties 总被引：2，自引：0，他引：2 
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下载免费PDF全文 Recent advances in sediment fingerprinting research have seen Bayesian mixing models being increasingly employed as an effective method to coherently translate component uncertainties into source apportionment results. Here, we advance earlier work by presenting an extended Bayesian mixing model capable of providing a full Bayes treatment of geochemical uncertainties. The performance of the extended full Bayes model was assessed against the equivalent empirical Bayes model and traditional frequentist optimisation. The performance of models coded in different Bayesian software (JAGS and Stan) was also evaluated, alongside an assessment of model sensitivity to reduced source representativeness and nonconservative fingerprint behaviour. Results revealed comparable accuracy and precision for the full and empirical Bayes models across both synthetic and real sediment geochemistry datasets, demonstrating that the empirical treatment of source data here represents a close approximation of the full Bayes treatment. Contrasts in the performance of models coded in JAGS and Stan revealed that the choice of software employed can impact significantly upon source apportionment results. Bayesian models coded in Stan were the least sensitive to both reduced source representativeness and nonconservative fingerprint behaviour, indicating Stan as the preferred software for future Bayesian sediment fingerprinting studies. Whilst the frequentist optimisation generally yielded comparable accuracy to the Bayesian models, uncertainties around apportionment estimates were substantially greater and the frequentist model was less effective at dealing with nonconservative behaviour. Overall, the effective performance of the extended full Bayes mixing model coded in Stan represents a notable advancement in source apportionment modelling relative to previous approaches. Both the mixing model and the software comparisons presented here should provide useful guidelines for future sediment fingerprinting studies. 相似文献
6.
M.A. Wibrin P. Bogaert D. Fasbender 《Stochastic Environmental Research and Risk Assessment (SERRA)》2006,20(6):423-433
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
7.
Spatio-temporal estimation of precipitation over a region is essential to the modeling of hydrologic processes for water resources management. The changes of magnitude and space–time heterogeneity of rainfall observations make space–time estimation of precipitation a challenging task. In this paper we propose a Box–Cox transformed hierarchical Bayesian multivariate spatio-temporal interpolation method for the skewed response variable. The proposed method is applied to estimate space–time monthly precipitation in the monsoon periods during 1974–2000, and 27-year monthly average precipitation data are obtained from 51 stations in Pakistan. The results of transformed hierarchical Bayesian multivariate spatio-temporal interpolation are compared to those of non-transformed hierarchical Bayesian interpolation by using cross-validation. The software developed by [11] is used for Bayesian non-stationary multivariate space–time interpolation. It is observed that the transformed hierarchical Bayesian method provides more accuracy than the non-transformed hierarchical Bayesian method. 相似文献
8.
A problem frequently met in engineering hydrology is the forecasting of hydrological variables conditional on their historical observations and the hindcasts and forecasts of a deterministic model. On the contrary, it is a common practice for climatologists to use the output of general circulation models (GCMs) for the prediction of climatic variables despite their inability to quantify the uncertainty of the predictions. Here we apply the well-established Bayesian processor of forecasts (BPF) for forecasting hydroclimatic variables using stochastic models through coupling them with GCMs. We extend the BPF to cases where long-term persistence appears, using the Hurst-Kolmogorov process (HKp, also known as fractional Gaussian noise) and we investigate its properties analytically. We apply the framework to calculate the distributions of the mean annual temperature and precipitation stochastic processes for the time period 2016–2100 in the United States of America conditional on historical observations and the respective output of GCMs. 相似文献
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Jürgen Pilz Gunter Spöck 《Stochastic Environmental Research and Risk Assessment (SERRA)》2008,22(5):621-632
The spatial prediction methodology that has become known under the heading of kriging is largely based on the assumptions
that the underlying random field is Gaussian and the covariance function is exactly known. In practical applications, however,
these assumptions will not hold. Beyond Gaussianity of the random field, lognormal kriging, disjunctive kriging, (generalized
linear) model-based kriging and trans-Gaussian kriging have been proposed in the literature. The latter approach makes use
of the Box–Cox-transform of the data. Still, all the alternatives mentioned do not take into account the uncertainty with
respect to the distribution (or transformation) and the estimated covariance function of the data. The Bayesian trans-Gaussian
kriging methodology proposed in the present paper is in the spirit of the “Bayesian bootstrap” idea advocated by Rubin (Ann
Stat 9:130–134, 1981) and avoids the unusual specification of noninformative priors often made in the literature and is entirely based on the
sample distribution of the estimators of the covariance function and of the Box–Cox parameter. After some notes on Bayesian
spatial prediction, noninformative priors and developing our new methodology finally we will present an example illustrating
our pragmatic approach to Bayesian prediction by means of a simulated data set. 相似文献
10.
K. K. Lee J. H. Cushman 《Stochastic Environmental Research and Risk Assessment (SERRA)》1993,7(4):241-253
An inverse problem is posed in terms of log-conductivities which are decomposed into macroscale deterministic and microscale stochastic components. The macroscale and microscale conductivities conceptualize hierarchical, scale-dependent aquifer parameters. A deterministic parameter estimation scheme divides a flow domain into a limited number of macroscale constant conductivity zones. A stochastic microscale parameter estimation scheme is used to obtain fluctuations about the macroscale averages in terms of geostatistical models. Both the macroscale and the microscale conductivities are estimated via maximum likelihood, adjoint-state methodologies. Monte Carlo-type approaches are used to examine the distribution of macroscale and microscale conductivity estimates. 相似文献
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Parameter uncertainty in hydrologic modeling is crucial to the flood simulation and forecasting. The Bayesian approach allows one to estimate parameters according to prior expert knowledge as well as observational data about model parameter values. This study assesses the performance of two popular uncertainty analysis (UA) techniques, i.e., generalized likelihood uncertainty estimation (GLUE) and Bayesian method implemented with the Markov chain Monte Carlo sampling algorithm, in evaluating model parameter uncertainty in flood simulations. These two methods were applied to the semi-distributed Topographic hydrologic model (TOPMODEL) that includes five parameters. A case study was carried out for a small humid catchment in the southeastern China. The performance assessment of the GLUE and Bayesian methods were conducted with advanced tools suited for probabilistic simulations of continuous variables such as streamflow. Graphical tools and scalar metrics were used to test several attributes of the simulation quality of selected flood events: deterministic accuracy and the accuracy of 95 % prediction probability uncertainty band (95PPU). Sensitivity analysis was conducted to identify sensitive parameters that largely affect the model output results. Subsequently, the GLUE and Bayesian methods were used to analyze the uncertainty of sensitive parameters and further to produce their posterior distributions. Based on their posterior parameter samples, TOPMODEL’s simulations and the corresponding UA results were conducted. Results show that the form of exponential decline in conductivity and the overland flow routing velocity were sensitive parameters in TOPMODEL in our case. Small changes in these two parameters would lead to large differences in flood simulation results. Results also suggest that, for both UA techniques, most of streamflow observations were bracketed by 95PPU with the containing ratio value larger than 80 %. In comparison, GLUE gave narrower prediction uncertainty bands than the Bayesian method. It was found that the mode estimates of parameter posterior distributions are suitable to result in better performance of deterministic outputs than the 50 % percentiles for both the GLUE and Bayesian analyses. In addition, the simulation results calibrated with Rosenbrock optimization algorithm show a better agreement with the observations than the UA’s 50 % percentiles but slightly worse than the hydrographs from the mode estimates. The results clearly emphasize the importance of using model uncertainty diagnostic approaches in flood simulations. 相似文献
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A Bayesian approach to characterize the predictive uncertainty in the delineation of time-related well capture zones in heterogeneous formations is presented and compared with the classical or non-Bayesian approach. The transmissivity field is modelled as a random space function and conditioned on distributed measurements of the transmissivity. In conventional geostatistical methods the mean value of the log transmissivity and the functional form of the covariance and its parameters are estimated from the available measurements, and then entered into the prediction equations as if they are the true values. However, this classical approach accounts only for the uncertainty that stems from the lack of ability to exactly predict the transmissivity at unmeasured locations. In reality, the number of measurements used to infer the statistical properties of the transmissvity field is often limited, which introduces error in the estimation of the structural parameters. The method presented accounts for the uncertainty that originates from the imperfect knowledge of the parameters by treating them as random variables. In particular, we use Bayesian methods of inference so as to make proper allowance for the uncertainty associated with estimating the unknown values of the parameters. The classical and Bayesian approach to stochastic capture zone delineation are detailed and applied to a hypothetical flow field. Two different sampling densities on a regular grid are considered to evaluate the effect of data density in both methods. Results indicate that the predictions of the Bayesian approach are more conservative. 相似文献
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Mingjie Chen Zhiming Lu George A. Zyvoloski 《Stochastic Environmental Research and Risk Assessment (SERRA)》2008,22(4):587-596
This study is an extension of the stochastic analysis of transient two-phase flow in randomly heterogeneous porous media (Chen
et al. in Water Resour Res 42:W03425, 2006), by incorporating direct measurements of the random soil properties. The log-transformed intrinsic permeability, soil pore
size distribution parameter, and van Genuchten fitting parameter are treated as stochastic variables that are normally distributed
with a separable exponential covariance model. These three random variables conditioned on given measurements are decomposed
via Karhunen–Loève decomposition. Combined with the conditional eigenvalues and eigenfunctions of random variables, we conduct
a series of numerical simulations using stochastic transient water–oil flow model (Chen et al. in Water Resour Res 42:W03425,
2006) based on the KLME approach to investigate how the number and location of measurement points, different random soil properties,
as well as the correlation length of the random soil properties, affect the stochastic behavior of water and oil flow in heterogeneous
porous media. 相似文献
14.
高斯混合模型(Gaussian Mixture Model, GMM)可以用来描述储层性质的多峰分布特性,多峰特性主要是由于它们在不同离散变量内的变化而引起的.在高斯混合模型中,高斯分量的权值代表离散变量的概率.然而,基于高斯混合模型的贝叶斯线性反演可能会对某些点的离散变量错误地分类,进而影响连续变量的反演结果,尤其存在强噪声的时候.在本文中,我们考虑了离散变量的空间变化性,并将高斯混合模型与序贯指示模拟(Sequential Indicator Simulation, SIS)相结合来确定离散变量的后验条件权值,形成了结合序贯指示模拟的贝叶斯高斯混合线性反演方法.该方法能够准确地对离散变量进行归类,且具有良好的抗噪性.通过模型试算,我们证明了这种方法的可行性,并在实际资料中取得了较好的结果. 相似文献
15.
This work introduces a new variational Bayes data assimilation method for the stochastic estimation of precipitation dynamics using radar observations for short term probabilistic forecasting (nowcasting). A previously developed spatial rainfall model based on the decomposition of the observed precipitation field using a basis function expansion captures the precipitation intensity from radar images as a set of ‘rain cells’. The prior distributions for the basis function parameters are carefully chosen to have a conjugate structure for the precipitation field model to allow a novel variational Bayes method to be applied to estimate the posterior distributions in closed form, based on solving an optimisation problem, in a spirit similar to 3D VAR analysis, but seeking approximations to the posterior distribution rather than simply the most probable state. A hierarchical Kalman filter is used to estimate the advection field based on the assimilated precipitation fields at two times. The model is applied to tracking precipitation dynamics in a realistic setting, using UK Met Office radar data from both a summer convective event and a winter frontal event. The performance of the model is assessed both traditionally and using probabilistic measures of fit based on ROC curves. The model is shown to provide very good assimilation characteristics, and promising forecast skill. Improvements to the forecasting scheme are discussed. 相似文献
16.
Understanding the geological uncertainty of hydrostratigraphic models is important for risk assessment in hydrogeology. An important feature of sedimentary deposits is the directional ordering of hydrostratigraphic units (HSU). Geostatistical simulation methods propose efficient algorithm for assessing HSU uncertainty. Among different geostatistical methods to simulate categorical data, Bayesian maximum entropy method (BME) and its simplified version Markov-type categorical prediction (MCP) present interesting features. In particular, the zero-forcing property of BME and MCP can provide a valuable constrain on directional properties. We illustrate the ability of MCP to simulate vertically ordered units. A regional hydrostratigraphic system with 11 HSU and different abundances is used. The transitional deterministic model of this system presents lateral variations and vertical ordering. The set of 66 (11 × 12/2) bivariate probability functions is directly calculated on the deterministic model with fast Fourier transform. Despite the trends present in the deterministic model, MCP is unbiased for the HSU proportions in the non-conditional case. In the conditional cases, MCP proved robust to datasets over-representing some HSU. The inter-realizations variability is shown to closely follow the amount and quality of data provided. Our results with different conditioning datasets show that MCP replicates adequately the directional units arrangement. Thus, MCP appears to be a practical method for generating stochastic models in a 3D hydrostratigraphic context. 相似文献
17.
ABSTRACTA parameter estimation strategy for a conceptual rainfall–runoff (CRR) model applied to a storm sewer system in an urban catchment (Chassieu, Lyon, France) is proposed on the basis of event-by-event Bayesian local calibrations. The marginal distribution formed by locally-estimated parameters is divided into conditional functions, clustering the event-based parameters based on their transferability to similar rainfall events. The conditional functions showed to be consistent with an observed bimodality in the marginal representation, reflecting two different hydrological conditions mainly related to the magnitude of the rainfall intensities (high or low). The improvements achieved by expressing the parameter probability functions into a conditional form are shown in terms of accuracy (Nash-Sutcliffe efficiency criterion), precision (average relative interval length) and reliability (percentage of coverage) for simulating flow rate in 255 and 110 calibration/verification events. 相似文献
18.
Robert Haining Jane Law Ravi Maheswaran Tim Pearson Paul Brindley 《Stochastic Environmental Research and Risk Assessment (SERRA)》2007,21(5):501-509
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
(NOx) 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 NOx 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. NOx effects apparently are significant at the two highest levels according to both modelling frameworks.
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| Paul BrindleyEmail: |
19.
We focus on the Bayesian estimation of strongly heterogeneous transmissivity fields conditional on data sampled at a set of locations in an aquifer. Log-transmissivity, Y, is modeled as a stochastic Gaussian process, parameterized through a truncated Karhunen–Loève (KL) expansion. We consider Y fields characterized by a short correlation scale as compared to the size of the observed domain. These systems are associated with a KL decomposition which still requires a high number of parameters, thus hampering the efficiency of the Bayesian estimation of the underlying stochastic field. The distinctive aim of this work is to present an efficient approach for the stochastic inverse modeling of fully saturated groundwater flow in these types of strongly heterogeneous domains. The methodology is grounded on the construction of an optimal sparse KL decomposition which is achieved by retaining only a limited set of modes in the expansion. Mode selection is driven by model selection criteria and is conditional on available data of hydraulic heads and (optionally) Y. Bayesian inversion of the optimal sparse KLE is then inferred using Markov Chain Monte Carlo (MCMC) samplers. As a test bed, we illustrate our approach by way of a suite of computational examples where noisy head and Y values are sampled from a given randomly generated system. Our findings suggest that the proposed methodology yields a globally satisfactory inversion of the stochastic head and Y fields. Comparison of reference values against the corresponding MCMC predictive distributions suggests that observed values are well reproduced in a probabilistic sense. In a few cases, reference values at some unsampled locations (typically far from measurements) are not captured by the posterior probability distributions. In these cases, the quality of the estimation could be improved, e.g., by increasing the number of measurements and/or the threshold for the selection of KL modes. 相似文献
20.
A partially non-ergodic ground-motion prediction equation is estimated for Europe and the Middle East. Therefore, a hierarchical model is presented that accounts for regional differences. For this purpose, the scaling of ground-motion intensity measures is assumed to be similar, but not identical in different regions. This is achieved by assuming a hierarchical model, where some coefficients are treated as random variables which are sampled from an underlying global distribution. The coefficients are estimated by Bayesian inference. This allows one to estimate the epistemic uncertainty in the coefficients, and consequently in model predictions, in a rigorous way. The model is estimated based on peak ground acceleration data from nine different European/Middle Eastern regions. There are large differences in the amount of earthquakes and records in the different regions. However, due to the hierarchical nature of the model, regions with only few data points borrow strength from other regions with more data. This makes it possible to estimate a separate set of coefficients for all regions. Different regionalized models are compared, for which different coefficients are assumed to be regionally dependent. Results show that regionalizing the coefficients for magnitude and distance scaling leads to better performance of the models. The models for all regions are physically sound, even if only very few earthquakes comprise one region. 相似文献