Applications of linear and nonlinear models fixed effects, random effects, and total least squares / [electronic resource] :

• 作者： Grafarend, Erik W.
• 其他作者：
  • Zwanzig, Silvelyn.
  • Awange, Joseph L.
  • SpringerLink (Online service)
• 其他題名：
  • Springer geophysics.
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 版本：Second edition.
• 叢書名： Springer geophysics,
• 主題： Geophysics--Mathematical models. , Regression analysis. , Linear models (Statistics) , Geology. , Linear Algebra. , Statistical Theory and Methods. , Surveying.
• ISBN： 9783030945985 (electronic bk.) 、 9783030945978 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: The First Problem of Algebraic Regression -- The First problem of probabilistic regression - the bias problem -- The second problem of algebraic regression - inconsistent system of linear observational equations -- The second problem of probabilistic regression- special Gauss-Markov model without datum defect - Setup of BLUUE for the moments of first order and of BIQUUE for the central moment of second order -- The third problem of probabilistic regression - special Gauss - Markov model with datum problem -Setup of BLUMBE and BLE for the moments of first order and of BIQUUE and BIQE for the central moment of second order.
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• 摘要註: This book provides numerous examples of linear and nonlinear model applications. Here, we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view and a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss-Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters, we concentrate on underdetermined and overdetermined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE, and total least squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so-called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann-Plucker coordinates, criterion matrices of type Taylor-Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overjet. This second edition adds three new chapters: (1) Chapter on integer least squares that covers (i) model for positioning as a mixed integer linear model which includes integer parameters. (ii) The general integer least squares problem is formulated, and the optimality of the least squares solution is shown. (iii) The relation to the closest vector problem is considered, and the notion of reduced lattice basis is introduced. (iv) The famous LLL algorithm for generating a Lovasz reduced basis is explained. (2) Bayes methods that covers (i) general principle of Bayesian modeling. Explain the notion of prior distribution and posterior distribution. Choose the pragmatic approach for exploring the a
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