![]() ![]() (3) Error-in-variables models, which cover: (i) Introduce the error-in-variables (EIV) model, discuss the difference to least squares estimators (LSE), (ii) calculate the total least squares (TLS) estimator. Useful in case of nonlinear models or linear models with no normal distribution: Monte Carlo (MC), Markov chain Monte Carlo (MCMC), approximative Bayesian computation (ABC) methods. (ii) Present the Bayes methods for linear models with normal distributed errors, including noninformative priors, conjugate priors, normal gamma distributions and (iii) short outview to modern application of Bayesian modeling. Choose the pragmatic approach for exploring the advantages of iterative Bayesian calculations and hierarchical modeling. Explain the notion of prior distribution and posterior distribution. (2) Bayes methods that covers (i) general principle of Bayesian modeling. (iv) The famous LLL algorithm for generating a Lovasz reduced basis is explained. (iii) The relation to the closest vector problem is considered, and the notion of reduced lattice basis is introduced. (ii) The general integer least squares problem is formulated, and the optimality of the least squares solution is shown. ![]() (1) Chapter on integer least squares that covers (i) model for positioning as a mixed integer linear model which includes integer parameters. This second edition adds three new chapters: Chapter seven is a speciality in the treatment of an overjet. 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. 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. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE, and total least squares. In the first six chapters, we concentrate on underdetermined and overdetermined linear systems as well as systems with a datum defect. While BLUUE is a stochastic regression model, LESS is an algebraic solution. 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. Our point of view is both an algebraic view and a stochastic one. Here, we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. This book provides numerous examples of linear and nonlinear model applications. ![]()
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |