共查询到20条相似文献，搜索用时 31 毫秒
1.
T. N. Kaseke M. E. Thompson 《Stochastic Environmental Research and Risk Assessment (SERRA)》1997,11(1):1-16
Abstract: Linear continuous time stochastic Nash cascade conceptual models for runoff are developed. The runoff is modeled
as a simple system of linear stochastic differential equations driven by white Gaussian and marked point process noises. In
the case of d reservoirs, the outputs of these reservoirs form a d dimensional vector Markov process, of which only the dth
coordinate process is observed, usually at a discrete sample of time points. The dth coordinate process is not Markovian.
Thus runoff is a partially observed Markov process if it is modeled using the stochastic Nash cascade model. We consider how
to estimate the parameters in such models. In principle, maximum likelihood estimation for the complete process parameters
can be carried out directly or through some form of the EM (estimation and maximization) algorithm or variation thereof, applied
to the observed process data. In this research we consider a direct approximate likelihood approach and a filtering approach
to an algorithm of EM type, as developed in Thompson and Kaseke (1994). These two methods are applied to some real life runoff
data from a catchment in Wales, England. We also consider a special case of the martingale estimating function approach on
the runoff model in the presence of rainfall. Finally, some simulations of the runoff process are given based on the estimated
parameters. 相似文献
2.
Environmental data are commonly constrained by a detection limit (DL) because of the restriction of experimental apparatus. In particular due to the changes of experimental units or assay methods, the observed data are often cut off by more than one DL. Measurements below the DLs are typically replaced by an arbitrary value such as zeros, half of DLs, or DLs for convenience of analysis. However, this method is widely considered unreliable and prone to bias. In contrast, maximum likelihood estimation (MLE) method for censored data has been developed for better performance and statistical justification. However, the existing MLE methods seldom address the multivariate context of censored environmental data especially for water quality. This paper proposes using a mixture model to flexibly approximate the underlying distribution of the observed data due to its good approximation capability and generation mechanism. In particular, Gaussian mixture model (GMM) is mainly focused in this study. To cope with the censored data with multiple DLs, an expectation–maximization (EM) algorithm in a multivariate setting is developed. The proposed statistical analysis approach is verified from both the simulated data and real water quality data. 相似文献
3.
结合随机状态空间方程和极大似然法的期望最大EM算法进行了结构运行模态分析。EM算法以迭代的方式更新模型参数,进而得到状态空间方程的极大似然估计。模态参数通过状态空间模型参数求得。应用了平方根卡尔曼滤波方程提高EM迭代过程的计算稳健性。考虑到状态空间方程中激励噪声和测量噪声的相关性,建立了更完善的参数化状态空间方程。通过数值模拟对比分析,结果表明：考虑噪声相关性的EM算法比假设噪声不相关的EM算法具有更高的识别精度,EM算法在采样数据较少的情况下比随机子空间方法更有优势。 相似文献
4.
Z. T. Yucel R. H. Shumway 《Stochastic Environmental Research and Risk Assessment (SERRA)》1996,10(2):107-126
This paper is concerned with developing computational methods and approximations for maximum likelihood estimation and minimum mean square error smoothing of irregularly observed two-dimensional stationary spatial processes. The approximations are based on various Fourier expansions of the covariance function of the spatial process, expressed in terms of the inverse discrete Fourier transform of the spectral density function of the underlying spatial process. We assume that the underlying spatial process is governed by elliptic stochastic partial differential equations (SPDE's) driven by a Gaussian white noise process. SPDE's have often been used to model the underlying physical phenomenon and the elliptic SPDE's are generally associated with steady-state problems.A central problem in estimation of underlying model parameters is to identify the covariance function of the process. The cumbersome exact analytical calculation of the covariance function by inverting the spectral density function of the process, has commonly been used in the literature. The present work develops various Fourier approximations for the covariance function of the underlying process which are in easily computable form and allow easy application of Newton-type algorithms for maximum likelihood estimation of the model parameters. This work also develops an iterative search algorithm which combines the Gauss-Newton algorithm and a type of generalized expectation-maximization (EM) algorithm, namely expectation-conditional maximization (ECM) algorithm, for maximum likelihood estimation of the parameters.We analyze the accuracy of the covariance function approximations for the spatial autoregressive-moving average (ARMA) models analyzed in Vecchia (1988) and illustrate the performance of our iterative search algorithm in obtaining the maximum likelihood estimation of the model parameters on simulated and actual data. 相似文献
5.
This paper presents a new identification technique for the extraction of modal parameters of structural systems subjected to base excitation. The technique uses output‐only measurements of the structural response. A combined subspace‐maximum likelihood algorithm is developed and applied to a three‐degree‐of‐freedom simulation model. Five ensembles of synthetically generated input signals, representing varying input characteristics, are employed in Monte Carlo simulations to illustrate the applicability of the method. The technique is able to circumvent some of the difficulties arising from short data sets by employing the Expectation Maximization (EM) algorithm to refine the subspace state estimates. This approach is motivated by successful application by previous authors on speech signals. Results indicate that, for certain system characteristics, more accurate pole estimates can be identified using the combined subspace‐EM formulation. In general, the damping ratios of the system are difficult to identify accurately due to limitations on data set length. The applicability of the technique to structural vibration signals is illustrated through the identification of seismic response data from the Vincent Thomas Bridge. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
6.
长波长假设条件下,各向同性背景地层中发育一组平行排列的垂直裂缝可等效为具有水平对称轴的横向各向同性（HTI）介质.基于不同观测方位的岩石地震响应特征变化,宽方位地震数据不仅可实现裂缝岩石弹性参数与各向异性参数的预测,同时也蕴含着丰富的孔隙度等储层物性参数信息.本文结合实际地震资料提出了贝叶斯框架下岩石物理驱动的储层裂缝参数与物性参数概率地震联合反演方法,首先基于AVAZ反演裂缝岩石的弹性参数与各向异性参数,并在此基础上通过统计岩石物理模型表征孔隙度、裂缝密度等各向异性介质储层参数与裂缝岩石参数的相互关联,并采用马尔科夫链蒙特卡洛（MCMC）抽样方法进行大量样本的随机模拟,使用期望最大化（EM）算法估计后验条件概率分布,最终寻找最大后验条件概率对应的孔隙度、裂缝密度等HTI裂缝介质储层参数即为反演结果.测井及实际地震数据处理表明,该方法能够稳定合理地从方位地震资料中获取裂缝岩石弹性参数与各向异性参数,并提供了一种较为可靠的孔隙度、裂缝密度等裂缝介质储层参数概率地震反演方法. 相似文献
7.
Antonello Maruotti Antonio Punzo Gianluca Mastrantonio Francesco Lagona 《Stochastic Environmental Research and Risk Assessment (SERRA)》2016,30(6):1725-1740
The modelling of animal movement is an important ecological and environmental issue. It is well-known that animals change their movement patterns over time, according to observable and unobservable factors. To trace the dynamics of behaviors, to identify factors influencing these dynamics and unobserved characteristics driving intra-subjects correlations, we introduce a time-dependent mixed effects projected normal regression model. A set of animal-specific parameters following a hidden Markov chain is introduced to deal with unobserved heterogeneity. For the maximum likelihood estimation of the model parameters, we outline an expectation–maximization algorithm. A large-scale simulation study provides evidence on model behavior. The data analysis approach based on the proposed model is finally illustrated by an application to a dataset, which derives from a population of Talitrus saltator from the beach of Castiglione della Pescaia (Italy). 相似文献
8.
Scale recursive estimation (SRE) is adopted for short term quantitative precipitation forecast (QPF). The precipitation field is modelled using a lognormal random cascade, well suited to properly represent the scaling properties of rainfall fields. To estimate the random cascade parameters, scale recursive maximum likelihood estimation (MLE) is carried out by the iterative expectation maximization (EM) algorithm. To illustrate the potentiality of the SRE, forecast of a synthetically generated rainfall time series is shown. Adaptive estimation of the process parameters is carried out and precipitation forecasts are issued. The forecasts from the SRE are compared with those from standard ARMA models, showing a good performance. The SRE is then adopted for forecasting of an observed half hourly precipitation series for a two day storm event in northern Italy. The SRE provides good performance and it can therefore be adopted as a tool for short term QPF. 相似文献
9.
10.
The increasing effort to develop and apply nonstationary models in hydrologic frequency analyses under changing environmental conditions can be frustrated when the additional uncertainty related to the model complexity is accounted for along with the sampling uncertainty. In order to show the practical implications and possible problems of using nonstationary models and provide critical guidelines, in this study we review the main tools developed in this field (such as nonstationary distribution functions, return periods, and risk of failure) highlighting advantages and disadvantages. The discussion is supported by three case studies that revise three illustrative examples reported in the scientific and technical literature referring to the Little Sugar Creek (at Charlotte, North Carolina), Red River of the North (North Dakota/Minnesota), and the Assunpink Creek (at Trenton, New Jersey). The uncertainty of the results is assessed by complementing point estimates with confidence intervals (CIs) and emphasizing critical aspects such as the subjectivity affecting the choice of the models’ structure. Our results show that (1) nonstationary frequency analyses should not only be based on at-site time series but require additional information and detailed exploratory data analyses (EDA); (2) as nonstationary models imply that the time-varying model structure holds true for the entire future design life period, an appropriate modeling strategy requires that EDA identifies a well-defined deterministic mechanism leading the examined process; (3) when the model structure cannot be inferred in a deductive manner and nonstationary models are fitted by inductive inference, model structure introduces an additional source of uncertainty so that the resulting nonstationary models can provide no practical enhancement of the credibility and accuracy of the predicted extreme quantiles, whereas possible model misspecification can easily lead to physically inconsistent results; (4) when the model structure is uncertain, stationary models and a suitable assessment of the uncertainty accounting for possible temporal persistence should be retained as more theoretically coherent and reliable options for practical applications in real-world design and management problems; (5) a clear understanding of the actual probabilistic meaning of stationary and nonstationary return periods and risk of failure is required for a correct risk assessment and communication. 相似文献
11.
A framework to estimate sediment loads based on the statistical distribution of sediment concentrations and various functional forms relating distribution characteristics (e.g. mean and variance) to covariates is developed. The covariates are used as surrogates to represent the main processes involved in sediment generation and transport. Statistical models of increasing complexity are built and compared to assess their relative performance using available sediment concentration and covariate data. Application to the Beaurivage River watershed (Québec, Canada) is conducted using data for the 1989–2004 period. The covariates considered in this application are streamflow and calendar day. A comparison of different statistical models shows that, in this case, the log‐normal distribution with a mean value depending on streamflow (power law with an additive term) and calendar day (sinusoidal), a constant coefficient of variation for streamflow dependence and a constant standard deviation for calendar day dependence provide the best result. Model parameters are estimated using the maximum likelihood estimation technique. The selected model is then used to estimate the distribution of annual sediment loads for the Beaurivage River watershed for a selected period. A bootstrap parametric method is implemented to account for uncertainties in parameter values and to build the distributions of annual loads. Comparison of model results with estimates obtained using the empirical ratio estimator shows that the latter were rarely within the 0·1–0·9 quantile interval of the distributions obtained with the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
12.
A new information criterion, the extended information criterion (EIC) was applied in order to determine an optimum solution in simultaneous iterative reconstruction technique (SIRT) P-wave velocity tomography. The EIC is derived from information theory and statistics, and it measures the goodness-of-fit between the true (unknown) data distribution and the observed data distribution: the former gives the probability of data realization from the true (unknown) model, whereas the latter gives a probability of data realization calculated from a particular model of which parameters are estimated. The EIC is calculated using bootstrap statistics, a numerical technique for calculating statistical estimators. Bootstrap statistics enables us to obtain the bias between the log likelihood and the expected log likelihood, and then to obtain the expected log likelihood from the log likelihood. Since the EIC is obtained numerically, we can use it for most problems of model parameter estimation without employing the maximum likelihood method. Taking weak anisotropy into account, we reconstructed the P-wave velocity structure of a rock sample during water infiltration under differential stress loading conditions. The results indicate that we can remove unrealistic solutions sometimes encountered when too many iterations are made. In spite of much computation time, the EIC is a promising technique for the near future, prompted by the rapid progress in current computer technology. 相似文献
13.
Nonuniqueness in geophysical inverse problems is naturally resolved by incorporating prior information about unknown models into observed data. In practical estimation procedures, the prior information must be quantitatively expressed. We represent the prior information in the same form as observational equations, nonlinear equations with random errors in general, and treat as data. Then we may define a posterior probability density function of model parameters for given observed data and prior data, and use the maximum likelihood criterion to solve the problem. Supposing Gaussian errors both in observed data and prior data, we obtain a simple algorithm for iterative search to find the maximum likelihood estimates. We also obtain an asymptotic expression of covariance for estimation errors, which gives a good approximation to exact covariance when the estimated model is linearly close to a true model. We demonstrate that our approach is a general extension of various inverse methods dealing with Gaussian data. By way of example, we apply the new approach to a problem of inferring the final rupture state of the 1943 Tottori earthquake (M = 7.4) from coseismic geodetic data. The example shows that the use of sufficient prior information effectively suppresses both the nonuniqueness and the nonlinearity of the problem. 相似文献
14.
In order to interpret field data from small-loop electromagnetic (EM) instruments with fixed source–receiver separation, 1D inversion method is commonly used due to its efficiency with regard to computation costs. This application of 1D inversion is based on the assumption that small-offset broadband EM signals are insensitive to lateral resistivity variation. However, this assumption can be false when isolated conductive bodies such as man-made objects are embedded in the earth. Thus, we need to clarify the applicability of the 1D inversion method for small-loop EM data. In order to systematically analyze this conventional inversion approach, we developed a 2D EM inversion algorithm and verified this algorithm with a synthetic EM data set. 1D and 2D inversions were applied to synthetic and field EM data sets. The comparison of these inversion results shows that the resistivity distribution of the subsurface constructed by the 1D inversion approach can be distorted when the earth contains man-made objects, because they induce drastic variation of the resistivity distribution. By analyzing the integrated sensitivity of the small-loop EM method, we found that this pitfall of 1D inversion may be caused by the considerable sensitivity of the small-loop EM responses to lateral resistivity variation. However, the application of our 2D inversion algorithm to synthetic and field EM data sets demonstrate that the pitfall of 1D inversion due to man-made objects can be successfully alleviated. Thus, 2D EM inversion is strongly recommended for detecting conductive isolated bodies, such as man-made objects, whereas this approach may not always be essential for interpreting the EM field data. 相似文献
15.
在实际的AVO反演问题中,叠前数据体中的噪声或其他因素严重影响了AVO反演问题的适定性,而采用先验地质信息作为AVO反演问题的约束条件是解决AVO反演问题不适定的一种可行方法. 文中的似然函数采用了[WTBX]ι[WTBX]p范数的解,并用Cauchy分布表示先验模型参数的分布. 以此为基础,在反演中建立了测井数据的参数协方差矩阵对反演过程进行约束,并采用了共轭梯度算法实现多参数非线性的反演过程. 同时,为了提高反演精度,避免动校正拉伸及依赖于炮检距的调谐效应对参数估计的影响,反演采用动校前地震数据进行参数估计. 从应用效果分析来看,即使叠前道集的信噪比不高,反演的结果也能较好地与实际情况相匹配,为识别储层流体性质提供了新的手段. 相似文献
16.
Nermin Sarlak 《水文研究》2008,22(17):3403-3409
Classical autoregressive models (AR) have been used for forecasting streamflow data in spite of restrictive assumptions, such as the normality assumption for innovations. The main reason for making this assumption is the difficulties faced in finding model parameters for non‐normal distribution functions. However, the modified maximum likelihood (MML) procedure used for estimating autoregressive model parameters assumes a non‐normally distributed residual series. The aim in this study is to compare the performance of the AR(1) model with asymmetric innovations with that of the classical autoregressive model for hydrological annual data. The models considered are applied to annual streamflow data obtained from two streamflow gauging stations in K?z?l?rmak Basin, Turkey. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
17.
This study uses borehole geophysical log data of sonic velocity and electrical resistivity to estimate permeability in sandstones in the northern Galilee Basin, Queensland. The prior estimates of permeability are calculated according to the deterministic log–log linear empirical correlations between electrical resistivity and measured permeability. Both negative and positive relationships are influenced by the clay content. The prior estimates of permeability are updated in a Bayesian framework for three boreholes using both the cokriging (CK) method and a normal linear regression (NLR) approach to infer the likelihood function. The results show that the mean permeability estimated from the CK-based Bayesian method is in better agreement with the measured permeability when a fairly apparent linear relationship exists between the logarithm of permeability and sonic velocity. In contrast, the NLR-based Bayesian approach gives better estimates of permeability for boreholes where no linear relationship exists between logarithm permeability and sonic velocity. 相似文献
18.
常规AVO三参数反演是通过Zoeppritz方程的近似公式来建立AVO正演模拟的过程,然而在P波入射角过临界角和弹性参数在纵向上变化剧烈的情况下,Zoeppritz方程近似公式精度有限.针对这种情况,可以使用精确的Zoeppritz方程来构建反演目标函数,由于精确Zoeppritz方程中P波反射系数和弹性参数之间是一种复杂的非线性关系,通常解决途径是利用非线性的优化算法来进行数值计算,但是非线性优化算法的缺点是计算量过大;另外一种途径是利用广义线性反演的方法,通过泰勒一阶展开式将P波反射振幅展开后,用线性关系近似表达非线性关系,经过几次迭代后,在理论上可以达到很高的精度,但是广义线性反演算法的核心部分--Jacobian矩阵由于矩阵条件数过大,往往会造成反演算法的不稳定,其应用范围得到了限制.贝叶斯反演方法是通过引入模型参数的先验分布结合噪声的似然函数,生成模型参数的后验分布,通过求取模型参数的最大后验概率分布来得到模型参数的反演解,由于引入模型参数的先验分布信息,可以有效的降低反演的不适定问题.本文将两种反演算法的思想相结合,利用广义线性反演算法的思想,构建AVO正演模拟的过程来提高大角度地震数据反演的精度,同时结合贝叶斯理论,通过引入模型参数的先验分布信息构建反演目标函数的正则化项,可以有效降低由于Jacob矩阵条件数过大带来的反演不适定问题,该算法假设模型参数服从三变量柯西分布. 相似文献
19.
D. J. Dupuis 《Journal of Hydrology》1997,200(1-4):295-306
In Smith (1986, J. Hydrol. 86, 27–43), a family of statistical distributions and estimators for extreme values based on a fixed number r > = 1 of the largest annual events are presented. The method of estimation was numerical maximum likelihood. In this paper, we consider the robust estimation of parameters in such families of distributions. The estimation technique, which is based on optimal B-robust estimates, will assign weights to each observation and give estimates of the parameters based on the data which are well modeled by the distribution. Thus, observations which are not consistent with the proposed distribution can be identified and the validity of the model can be assessed. The method is illustrated on Venice sea level data. 相似文献
20.