Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.

Web Service Composition Systems for the Web Service Challenge - A Detailed Review

This report gives a detailed discussion on the system, algorithms, and techniques that we have applied in order to solve the Web Service Challenges (WSC) of the years 2006 and 2007. These international contests are focused on semantic web service composition. In each challenge of the contests, a repository of web services is given. The input and output parameters of the services in the repository are annotated with semantic concepts. A query to a semantic composition engine contains a set of available input concepts and a set of wanted output concepts. In order to employ an offered service for a requested role, the concepts of the input parameters of the offered operations must be more general than requested (contravariance). In contrast, the concepts of the output parameters of the offered service must be more specific than requested (covariance). The engine should respond to a query by providing a valid composition as fast as possible. We discuss three different methods for web service composition: an uninformed search in form of an IDDFS algorithm, a greedy informed search based on heuristic functions, and a multi-objective genetic algorithm.

Parameter identification of structural dynamic models by inverse statistical analysis

Auf dem Gebiet der Strukturdynamik sind computergestützte Modellvalidierungstechniken inzwischen weit verbreitet. Dabei werden experimentelle Modaldaten, um ein numerisches Modell für weitere Analysen zu korrigieren. Gleichwohl repräsentiert das validierte Modell nur das dynamische Verhalten der getesteten Struktur. In der Realität gibt es wiederum viele Faktoren, die zwangsläufig zu variierenden Ergebnissen von Modaltests führen werden: Sich verändernde Umgebungsbedingungen während eines Tests, leicht unterschiedliche Testaufbauten, ein Test an einer nominell gleichen aber anderen Struktur (z.B. aus der Serienfertigung), etc. Damit eine stochastische Simulation durchgeführt werden kann, muss eine Reihe von Annahmen für die verwendeten Zufallsvariablengetroffen werden. Folglich bedarf es einer inversen Methode, die es ermöglicht ein stochastisches Modell aus experimentellen Modaldaten zu identifizieren. Die Arbeit beschreibt die Entwicklung eines parameter-basierten Ansatzes, um stochastische Simulationsmodelle auf dem Gebiet der Strukturdynamik zu identifizieren. Die entwickelte Methode beruht auf Sensitivitäten erster Ordnung, mit denen Parametermittelwerte und Kovarianzen des numerischen Modells aus stochastischen experimentellen Modaldaten bestimmt werden können.