Showing papers on "Covariance mapping published in 2003"

Modelling the random effects covariance matrix in longitudinal data

Abstract: A common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed constant across subject. However, in many situations this matrix may differ by measured covariates. In this paper, we propose an approach to model the random effects covariance matrix by using a special Cholesky decomposition of the matrix. In particular, we will allow the parameters that result from this decomposition to depend on subject-specific covariates and also explore ways to parsimoniously model these parameters. An advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix. In addition, the parameters resulting from this decomposition have a sensible interpretation. We propose fully Bayesian modelling for which a simple Gibbs sampler can be implemented to sample from the posterior distribution of the parameters. We illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects.

Background error covariance functions for Doppler radial-wind analysis

Abstract: Under the assumption that the vector field of the background wind error is Gaussian random, homogeneous and isotropic in the horizontal, a two-dimensional form of error covariance function is derived for the radial component of the background wind projected onto the direction of radar beam at a low elevation. The derived covariance function is homogeneous but non-isotropic in the horizontal, and approximately homogeneous on the conical surface of low-elevation radar scans. This covariance function can be applied directly to statistical interpolation of radar-observed radial winds on the conical surface, although the true optimality of the analysis depends on the underlying assumption. It can also be used as an influence function for the radial-wind analysis with zero background. The structure of this covariance function is interpreted in terms of the influence of a single point observation on the radial-wind analysis. The utility and merits of this covariance function are demonstrated by numerical experiments. Copyright © 2003 Royal Meteorological Society

Gibbs sampler for computing and propagating large covariance matrices

Abstract: The use of sampling-based Monte Carlo methods for the computation and propagation of large covariance matrices in geodetic applications is investigated. In particular, the so-called Gibbs sampler, and its use in deriving covariance matrices by Monte Carlo integration, and in linear and nonlinear error propagation studies, is discussed. Modifications of this technique are given which improve in efficiency in situations where estimated parameters are highly correlated and normal matrices appear as ill-conditioned. This is a situation frequently encountered in satellite gravity field modelling. A synthetic experiment, where covariance matrices for spherical harmonic coefficients are estimated and propagated to geoid height covariance matrices, is described. In this case, the generated samples correspond to random realizations of errors of a gravity field model.

Three-mode analysis of multimode covariance matrices.

Abstract: Multimode covariance matrices, such as multitrait-multimethod matrices, contain the covariances of subject scores on variables for different occasions or conditions. This paper presents a comparison of three-mode component analysis and three-mode factor analysis applied to such covariance matrices. The differences and similarities between the non-stochastic and stochastic approaches are demonstrated by two examples, one of which has a longitudinal design. The empirical comparison is facilitated by deriving, as a heuristic device, a statistic based on the maximum likelihood function for three-mode factor analysis and its associated degrees of freedom for the three-mode component models. Furthermore, within the present context a case is made for interpreting the core array as second-order components.

Globally covering a-priori regional gravity covariance models

Abstract: . Gravity anomaly data generated using Wenzel’s GPM98A model complete to degree 1800, from which OSU91A has been subtracted, have been used to estimate covariance functions for a set of globally covering equal-area blocks of size 22.5° × 22.5° at Equator, having a 2.5° overlap. For each block an analytic covariance function model was determined. The models are based on 4 parameters: the depth to the Bjerhammar sphere (determines correlation), the free-air gravity anomaly variance, a scale factor of the OSU91A error degree-variances and a maximal summation index, N, of the error degree-variances. The depth of Bjerhammar-sphere varies from -134km to nearly zero, N varies from 360 to 40, the scale factor from 0.03 to 38.0 and the gravity variance from 1081 to 24(10µms-2)2. The parameters are interpreted in terms of the quality of the data used to construct OSU91A and GPM98A and general conditions such as the occurrence of mountain chains. The variation of the parameters show that it is necessary to use regional covariance models in order to obtain a realistic signal to noise ratio in global applications. Key words. GOCE mission, Covariance function, Spacewise approach`

Covariance functions and models for complex-valued random fields

Abstract: In Geostatistics, primary interest often lies in the study of the spatial, or spatial-temporal, correlation of real-valued random fields, anyway complex-valued random field theory is surely a natural extension of the real domain In such a case, it is useful to consider complex covariance functions which are composed of an even real part and an odd imaginary part Generating complex covariance functions is not simple at all, but the procedure, developed in this paper, allows generating permissible covariance functions for complex-valued random fields in a straightforward way In particular, by recalling the spectral representation of the covariance and translating the spectral density function by using a shifting factor, complex covariances are obtained Some general aspects and properties of complex-valued random fields and their moments are pointed out and some examples are given

Covariance mapping in matrix-assisted laser desorption/ionization time-of-flight mass spectrometry.

Abstract: A novel method for acquisition and numerical analysis of matrix-assisted laser desorption/ionization (MALDI) time-of-flight mass spectral data is described. The digitized ion current transient from each consecutive laser shot is first acquired and stored independently. Subsequently, statistical correlation parameters between all stored transients are computed. We illustrate the uses of this event-by-event analysis method for studies of sample surface heterogeneity as well as for elucidating the mechanisms of ion formation in MALDI. Other potential applications of the method are also outlined.

Universal kriging for spatio‐temporal data

Abstract: In this article we have used wide applicable classes of spatio‐temporal nonseparable and separable covariance models. One of the objectives of this paper is to furnish a possibility how to avoid the usage of complicated covariance functions. Assuming regression model for mean function the analytical expressions for the optimal linear prediction (universal kriging) and mean squared prediction error (MSPE) was obtained. Parameterized spatio‐temporal covariance functions were fitted for the real data. Prediction values and MSPE were presented. For visualization of results on graphics are used free available software Gstat.

Polynomial covariance functions on intervals

Abstract: A characteriztion is presented of the class of stationary processes that have polynomial covariance functions of degree less than or equal to 4 on an interval. The results extend to isotropic random fields and have applications in spatial statistics.

Mean, Variance, Covariance

Abstract: In this chapter the elementary concepts of mean, variance and covariance are presented. The expectation operator is introduced, which serves to compute these quantities in the framework of probabilistic models.

Estimation of locally stationary covariance matrices from data

Abstract: Local stationarity of an L/sup 2/(/spl Ropf/) bandpass random process reflects in specific regions of either the frequency plane of its 2 dimensional power spectrum or the time-frequency plane of its Wigner distribution. The paper addresses the problem of estimating from data a covariance matrix that satisfies the constraint of being locally stationary. We also show, with a real-data case study, the improvement in performance achieved by using locally stationary covariance matrices in the development of low cost quadratic detectors.

Characterization of fixed effects as special case of generalized random effects.

Abstract: The objective of this paper is to emphasize the common nature of fixed and random factors in a mixed linear statistical model. We show that factors can be classified into fixed and random factors by means of covariance matrices of their level effects. In particular, classical reparameterization conditions for fixed factors can be formulated in this way.

Error Covariance Estimation and Representation for Mesoscale Data Assimilation

Abstract: : The goal of this project is to explore and develop new methods of error covariance estimation and representation that can improve mesoscale data assimilation and numerical weather prediction. To this end, three research objectives were fulfilled: (i) A spline-spectral covariance model was developed to enhanced the capability of the innovation method for error covariance estimation. (ii) Non-isotropic error correlation functions were derived for radar radial-wind analysis and used to reformulate the innovation method. The reformulated method provided the first objective way to statistically estimate not only radar observation error variance but also observation error correlation between neighboring gates or beams of radar scans at very fine scales. (iii) By using the advanced functional approach and generalized Fourier transformation, the inverse of a covariance function was shown to be representable by a vector differential operator, called D-operator. With D-operator representations, the inverses error covariance matrices can be formulated directly and efficiently in the cost-functions of variational data assimilation.

Statistical Estimation and Classication on Commutative Covariance Structures 1

Abstract: Statistical inference is investigated under the following constraints on the covariance structure for the observation vector: covariance matrices belong to some commutative matrix algebra. Commutative approximation of arbitrary covariance structures and statistical estima- tion of the parameters of a given commutative structure are studied. The results are applied to statistical classication of Gaussian vectors having commutative covariance structure. Statistical formulations of the problems of control of an object, ltration of its phase vector or output signal, classication or clustering of statistical ensembles, and many other applied problems in statistical decision theory usually involve the choice of a probabilistic model for random (internal or external) factors acting on the controlled object or observation system. The range of covariance models for the components of random factors is rather wide; it extends from the simplest model of uncorrelated identically distributed components with a unique unknown parameter (variance) to a general model of arbitrarily correlated components with n(n +1 )=2 parameters, where n is the number of components. The agreement of a model with observation data need not necessarily grow with the complexity of the model. m P i=1 iAi ,w here