首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 535 毫秒
1.
Dynamic life tables arise as an alternative to the standard (static) life tables with the aim of incorporating the evolution of mortality over time. These tables can be considered as a two-way table on a grid equally spaced in either the vertical (age) or horizontal (year) directions, and the data can be decomposed into a deterministic large-scale variation (trend) plus a stochastic small-scale variation (residuals). In this context, space–time geostatistical methods can be used for fitting and predicting the dynamic mortality. We use four different space–time covariance functions for fitting and predicting mortality in Spain during the period 1980–2005. In particular, we aim at showing the behavior of separable versus nonseparable fitted structures on one hand, and the behavior of simple structures given by combinations of products and sums versus more complicated negative structures on the other hand.  相似文献   

2.
Radial basis functions with compact support for multivariate geostatistics   总被引：3，自引：3，他引：0  
Matrix-valued radially symmetric covariance functions (also called radial basis functions in the numerical analysis literature) are crucial for the analysis, inference and prediction of Gaussian vector-valued random fields. This paper provides different methodologies for the construction of matrix-valued mappings that are positive definite and compactly supported over the sphere of a d-dimensional space, of a given radius. In particular, we offer a representation based on scaled mixtures of Askey functions; we also suggest a method of construction based on B-splines. Finally, we show that the very appealing convolution arguments are indeed effective when working in one dimension, prohibitive in two and feasible, but substantially useless, when working in three dimensions. We exhibit the statistical performance of the proposed models through simulation study and then discuss the computational gains that come from our constructions when the parameters are estimated via maximum likelihood. We finally apply our constructions to a North American Pacific Northwest temperatures dataset.  相似文献   

3.
In statistical space-time modeling, the use of non-separable covariance functions is often more realistic than separable models. In the literature, various tests for separability may justify this choice. However, in case of rejection of the separability hypothesis, none of these tests include testing for the type of non-separability of space-time covariance functions. This is an important and further significant step for choosing a class of models. In this paper a method for testing positive and negative non-separability is given; moreover, an approach for testing some well known classes of space-time covariance function models has been proposed. The performance of the tests has been shown using real and simulated data.  相似文献   

4.
 Many heterogeneous media and environmental processes are statistically anisotropic. In this paper we focus on range anisotropy, that is, stochastic processes with variograms that have direction dependent correlation lengths and direction independent sill. We distinguish between two classes of anisotropic covariance models: Class (A) models are reducible to isotropic after rotation and rescaling operations. Class (B) models can be separated into a product of one-dimensional functions oriented along the principal axes. We propose a new Class (A) model with multiscale properties that has applications in subsurface hydrology. We also present a family of Class (B) models based on non-Euclidean distance metrics that are generated by superellipsoidal functions. Next, we propose a new method for determining the orientation of the principal axes and the degree of anisotropy, i.e., the ratio(s) of the correlation lengths. This information reduces the degrees of freedom of anisotropic variograms and thus simplifies the estimation procedure. In particular, Class (A) models are reduced to isotropic and Class (B) models to one-dimensional functions. Our method is based on an explicit relation between the second-rank slope tensor (SRST), which can be estimated from the data, and the covariance tensor. The procedure is conceptually simple and numerically efficient. It is more accurate for regular (on-grid) data distributions, but it can also be used for sparse (off-grid) spatial distributions. In the case of non-differentiable random fields the method can be extended using generalized derivatives. We illustrate its implementation with numerical simulations.  相似文献   

5.
Quasi arithmetic and Archimedean functionals are used to build new classes of spectral densities for processes defined on any d-dimensional lattice \mathbbZd{\mathbb{Z}^d} and random fields defined on the d-dimensional Euclidean space \mathbbRd{\mathbb{R}^d}, given simple margins. We discuss the mathematical features of the proposed constructions, and show rigorously as well as through examples, that these new classes of spectra generalize celebrated classes introduced in the literature. Additionally, we obtain permissible spectral densities as linear combinations of quasi arithmetic or Archimedean functionals, whose associated correlation functions may attain negative values or oscillate between positive and negative ones. We finally show that these new classes of spectral densities can be used for nonseparable processes that are not necessarily diagonally symmetric.  相似文献   

6.
Globally supported covariance functions are generally associated with dense covariance matrices, meaning severe numerical problems in solution feasibility. These problems can be alleviated by considering methods yielding sparse covariance matrices. Indeed, having many zero entries in the covariance matrix can both greatly reduce computer storage requirements and the number of floating point operations needed in computation. Compactly supported covariance functions considerably reduce the computational burden of kriging, and allow the use of computationally efficient sparse matrix techniques, thus becoming a core aspect in spatial prediction when dealing with massive data sets. However, most of the work done in the context of compactly supported covariance functions has been carried out in the stationary context. This assumption is not generally met in practical and real problems, and there has been a growing recognition of the need for non-stationary spatial covariance functions in a variety of disciplines. In this paper we present a new class of non-stationary, compactly supported spatial covariance functions, which adapts a class of convolution-based flexible models to non-stationary situations. Some particular examples, computational issues, and connections with existing models are considered.  相似文献   

7.
《Advances in water resources》2005,28(11):1171-1195
We extend lattice Boltzmann (LB) methods to advection and anisotropic-dispersion equations (AADE). LB methods are advocated for the exactness of their conservation laws, the handling of different length and time scales for flow/transport problems, their locality and extreme simplicity. Their extension to anisotropic collision operators (L-model) and anisotropic equilibrium distributions (E-model) allows to apply them to generic diffusion forms. The AADE in a conventional form can be solved by the L-model. Based on a link-type collision operator, the L-model specifies the coefficients of the symmetric diffusion tensor as linear combination of its eigenvalue functions. For any type of collision operator, the E-model constructs the coefficients of the transformed diffusion tensors from linear combinations of the relevant equilibrium projections. The model is able to eliminate the second order tensor of its numerical diffusion. Both models rely on mass conserving equilibrium functions and may enhance the accuracy and stability of the isotropic convection–diffusion LB models.The link basis is introduced as an alternative to a polynomial collision basis. They coincide for one particular eigenvalue configuration, the two-relaxation-time (TRT) collision operator, suitable for both mass and momentum conservation laws. TRT operator is equivalent to the BGK collision in simplicity but the additional collision freedom relates it to multiple-relaxation-times (MRT) models. “Optimal convection” and “optimal diffusion” eigenvalue solutions for the TRT E-model allow to remove next order corrections to AADE. Numerical results confirm the Chapman–Enskog and dispersion analysis.  相似文献   

8.
The properties of linear spatial interpolators of single realizations and trend components of regionalized variables are examined in this work. In the case of the single realization estimator explicit and exact expressions for the weighting vector and the variances of estimator and estimation error were obtained from a closed-form expression for the inverse of the Lagrangian matrix. The properties of the trend estimator followed directly from the Gauss-Markoff theorem. It was shown that the single realization estimator can be decomposed into two mutually orthogonal random functions of the data, one of which is the trend estimator. The implementation of liear spatial estimation was illustrated with three different methods, i.e., full information maximum likelihood (FIML), restricted maximum likelihood (RML), and Rao's minimum norm invariant quadratic unbiased estimation (MINQUE) for the single realization case and via generalized least squares (GLS) for the trend. The case study involved large correlation length-scale in the covariance of specific yield producing a nested covariance structure that was nearly positive semidefinite. The sensitivity of model parameters, i.e., drift and variance components (local and structured) to the correlation length-scale, choice of covariance model (i.e., exponential and spherical), and estimation method was examined. the same type of sensitivity analysis was conducted for the spatial interpolators. It is interesting that for this case study, characterized by a large correlation length-scale of about 50 mi (80 km), both parameter estimates and linear spatial interpolators were rather insensitive to the choice of covariance model and estimation method within the range of credible values obtained for the correlation length-scale, i.e., 40–60 mi (64–96 km), with alternative estimates falling within ±5% of each other.  相似文献   

9.
In geostatistical applications, the terms correlation length and range are often used interchangeably and refer to a characteristic covariance length ξ that normalizes the lag distance in the variogram or the covariance model. We present equations that strictly define the correlation length (r c ) and integral range (ℓ c ). We derive analytical expressions for r c and ℓ c of the Whittle–Matérn, fluctuation gradient curvature and rational quadratic covariances. For these covariances, we show that the correlation length and integral range for a given model are not fully determined by ξ. We define non-trivial covariance functions, and we formulate an ergodicity index based on ℓ c . We propose using the ergodicity index to compare coarse-grained measures corresponding to non-trivial covariance functions with different parameters. Finally, we discuss potential applications of the proposed covariance models in stochastic subsurface hydrology.  相似文献   

10.
A class of non-stationary covariance functions with compact support   总被引：1，自引：1，他引：0  
This article describes the use of non-stationary covariance functions with compact support to estimate and simulate a random function. Based on the kernel convolution theory, the functions are derived by convolving hyperspheres in \(\mathbb{R}^n\) followed by a Radon transform. The order of the Radon transform controls the differentiability of the covariance functions. By varying spatially the hyperspheres radius one defines non-stationary isotropic versions of the spherical, the cubic and the penta-spherical models. Closed-form expressions for the non-stationary covariances are derived for the isotropic spherical, cubic, and penta-spherical models. Simulation of the different non-stationary models is easily obtained by weighted average of independent standard Gaussian variates in both the isotropic and the anisotropic case. The non-stationary spherical covariance model is applied to estimate the overburden thickness over an area composed of two different geological domains. The results are compared to the estimation with a single stationary model and the estimation with two stationary models, one for each geological domain. It is shown that the non-stationary model enables a reduction of the mean square error and a more realistic transition between the two geological domains.  相似文献   

11.
This paper presents new ideas on sampling design and minimax prediction in a geostatistical model setting. Both presented methodologies are based on regression design ideas. For this reason the appendix of this paper gives an introduction to optimum Bayesian experimental design theory for linear regression models with uncorrelated errors. The presented methodologies and algorithms are then applied to the spatial setting of correlated random fields. To be specific, in Sect. 1 we will approximate an isotropic random field by means of a regression model with a large number of regression functions with random amplitudes, similarly to Fedorov and Flanagan (J Combat Inf Syst Sci: 23, 1997). These authors make use of the Karhunen Loeve approximation of the isotropic random field. We use the so-called polar spectral approximation instead; i.e. we approximate the isotropic random field by means of a regression model with sine-cosine-Bessel surface harmonics with random amplitudes and then, in accordance with Fedorov and Flanagan (J Combat Inf Syst Sci: 23, 1997), apply standard Bayesian experimental design algorithms to the resulting Bayesian regression model. Section 2 deals with minimax prediction when the covariance function is known to vary in some set of a priori plausible covariance functions. Using a minimax theorem due to Sion (Pac J Math 8:171–176, 1958) we are able to formulate the minimax problem as being equivalent to an optimum experimental design problem, too. This makes the whole experimental design apparatus available for finding minimax kriging predictors. Furthermore some hints are given, how the approach to spatial sampling design with one a priori fixed covariance function may be extended by means of minimax kriging to a whole set of a priori plausible covariance functions such that the resulting designs are robust. The theoretical developments are illustrated with two examples taken from radiological monitoring and soil science.  相似文献   

12.
In this paper, a new non-linear fuzzy-set based methodology is proposed to characterize and propagate uncertainty through a multiple linear regression (MLR) model to predict DO using flow and water temperature as the regressors. The output is depicted as probabilistic rather than deterministic and is used to calculate the risk of low DO concentration. To demonstrate the new method, data from the Bow River in Calgary, Alberta from 2006 to 2008 are used. Low DO concentration has been occasionally observed in the river and correctly predicting, and quantifying the associated uncertainty and variability of DO is of interest to the City of Calgary. Flow, temperature and DO data were used to construct five MLR models, using different combinations of linear and non-linear fuzzy membership functions. The results show that non-linear representation of variance is superior to the linear approach based on model performance. Normal and Gumbel based membership functions produced the best results. The outputs from two non-linear fuzzy membership models were used to calculate risk of low DO. The predicted risk was between 3.9 and 4.9 %. This is an improvement over the traditional method, which can not indicate a risk of low DO for the same time period. This study demonstrates that water resource managers can adequately use MLR models to predict the risk of low DO using abiotic factors.  相似文献   

13.
Spatial (two-dimensional) distributions in ecology are often influenced by spatial autocorrelation. In standard regression models, however, observations are assumed to be statistically independent. In this paper we present an alternative to other methods that allow for autocorrelation. We show that the theory of wavelets provides an efficient method to remove autocorrelations in regression models using data sampled on a regular grid. Wavelets are particularly suitable for data analysis without any prior knowledge of the underlying correlation structure. We illustrate our new method, called wavelet-revised model, by applying it to multiple regression for both normal linear models and logistic regression. Results are presented for computationally simulated data and real ecological data (distribution of species richness and distribution of the plant species Dianthus carthusianorum throughout Germany). These results are compared to those of generalized linear models and models based on generalized estimating equations. We recommend wavelet-revised models, in particular, as a method for logistic regression using large datasets.  相似文献   

14.
 Permissibility of a covariance function (in the sense of Bochner) depends on the norm (or metric) that determines spatial distance in several dimensions. A covariance function that is permissible for one norm may not be so for another. We prove that for a certain class of covariances of weakly homogeneous random fields, the spatial distance can be defined only in terms of the Euclidean norm. This class includes commonly used covariance functions. Functions that do not belong to this class may be permissible covariances for some non-Euclidean metric. Thus, a different class of covariances, for which non-Euclidean norms are valid spatial distances, is also discussed. The choice of a coordinate system and associated norm to describe a physical phenomenon depends on the nature of the properties being described. Norm-dependent permissibility analysis has important consequences in spatial statistics applications (e.g., spatial estimation or mapping), in which one is concerned about the validity of covariance functions associated with a physically meaningful norm (Euclidean or non-Euclidean).  相似文献   

15.
Although modeling of cross-covariances by fitting the linear model of coregionalization (LMC) is considered a cumbersome task, cross-covariances are the key for integration of data for multiple attributes in environmental hydrology, aquifer and reservoir characterizations using multivariate geostatistics. This paper proposes a novel method of modeling cross-covariances in the linear model of coregionalization (LMC). The classic minimum/maximum autocorrelation factors (MAF) method is analyzed and found to be a good tool to discriminate the elementary nested structures of directional sample covariance matrices. Thus, separate modeling of the scalar sample covariance for each MAF factor may allow to obtain the complete LMC model for the original attributes after a back rotation of the diagonal model covariance matrix of directional factors. However, such a back rotation is not computable following the classic MAF formulation. This paper introduces an ambi-rotational minimum/maximum autocorrelation factors (AMAF) method that allows a back and forth double rotation of the directional diagonal model covariance matrix for factors. This approach provides a device for modeling of the full matrix of directional covariance and cross-covariance for the original attributes in the LMC without recurring to iterations. In this way, the use of multivariate geostatistics for data integration is allowed avoiding collocated approaches or rotation and modeling of data factor scores. The method is illustrated with an example for covariances for three attributes.  相似文献   

16.
Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data.  相似文献   

17.
Saturation of porous rocks with a mixture of two fluids (known as partial saturation) has a substantial effect on the seismic waves propagating through these rocks. In particular, partial saturation causes significant attenuation and dispersion of the propagating waves, due to wave-induced fluid flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. As partial fluid saturation can occur on different length scales, attenuation due to wave-induced fluid flow is ubiquitous. In particular, mesoscopic fluid flow due to heterogeneities occurring on a scale greater than porescale, but less than wavelength scale, is responsible for significant attenuation in the frequency range from 10 to 1000 Hz.Most models of attenuation and dispersion due to mesoscopic heterogeneities imply that fluid heterogeneities are distributed in a periodic/regular way. In 1D this corresponds to periodically alternating layering, in 3D as periodically distributed inclusions of a given shape (usually spheres). All these models yield very similar estimates of attenuation and dispersion.Experimental studies show that mesoscopic heterogeneities have less idealized distributions and that the distribution itself affects attenuation and dispersion. Therefore, theoretical models are required which would simulate the effect of more general and realistic fluid distributions.We have developed two theoretical models which simulate the effect of random distributions of mesoscopic fluid heterogeneities. The first model assumes that one fluid forms a random ensemble of spherical inclusions in a porous medium saturated by the other fluid. The attenuation and dispersion predicted by this model are very similar to those predicted for 3D periodic distribution. Attenuation (inverse quality factor) is proportional to ω at low frequencies for both distributions. This is in contrast to the 1D case, where random and periodically alternating layering shows different attenuation behaviour at low frequencies. The second model, which assumes a 3D continuous distribution of fluid heterogeneities, also predicts the same low-frequency asymptote of attenuation. However, the shapes of the frequency dependencies of attenuation are different. As the 3D continuous random approach assumes that there will be a distribution of different patch sizes, it is expected to be better suited to modelling experimental results. Further research is required in order to uncover how to relate the random functions to experimentally significant parameters.  相似文献   

18.
This paper presents an algorithm for simulating Gaussian random fields with zero mean and non-stationary covariance functions. The simulated field is obtained as a weighted sum of cosine waves with random frequencies and random phases, with weights that depend on the location-specific spectral density associated with the target non-stationary covariance. The applicability and accuracy of the algorithm are illustrated through synthetic examples, in which scalar and vector random fields with non-stationary Gaussian, exponential, Matérn or compactly-supported covariance models are simulated.  相似文献   

19.
We present an efficient numerical method for solving stochastic porous media flow problems. Single-phase flow with a random conductivity field is considered in a standard first-order perturbation expansion framework. The numerical scheme, based on finite element techniques, is computationally more efficient than traditional approaches because one can work with a much coarser finite element mesh. This is achieved by avoiding the common finite element representation of the conductivity field. Computations with the random conductivity field only arise in integrals of the log conductivity covariance function. The method is demonstrated in several two- and three-dimensional flow situations and compared to analytical solutions and Monte Carlo simulations. Provided that the integrals involving the covariance of the log conductivity are computed by higher-order Gaussian quadrature rules, excellent results can be obtained with characteristic element sizes equal to about five correlation lengths of the log conductivity field. Investigations of the validity of the proposed first-order method are performed by comparing nonlinear Monte Carlo results with linear solutions. In box-shaped domains the log conductivity standard deviation σY may be as large as 1.5, while the head variance is considerably influenced by nonlinear effects as σY approaches unity in more general domains.  相似文献   

20.
The differentiability of a random field has a direct relationship with the differentiability of its covariance function. We review the concept of differentiability of space–time covariance models and random fields, and its implications on predictions. We analyze the change of behavior of the covariance function at the origin and at different space–time lags away from the origin, by using the concept of smoothness which can be considered the geometrical view of the differentiability. We propose a way to measure the smoothness of any covariance function, and apply it to purely spatial and space–time covariance functions.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号