Buch, Englisch, 1113 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 1891 g
Reihe: Springer Geophysics
Fixed Effects, Random Effects, and Total Least Squares
Buch, Englisch, 1113 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 1891 g
Reihe: Springer Geophysics
ISBN: 978-3-030-94600-5
Verlag: Springer International Publishing
(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 advantages of iterative Bayesian calculations and hierarchical modeling. (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. 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.
(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. Summarize the properties of TLS, (iii) explain the idea of simulation extrapolation (SIMEX) estimators, (iv) introduce the symmetrized SIMEX (SYMEX) estimator and its relation to TLS, and (v) short outview to nonlinear EIV models.
The chapter onalgebraic solution of nonlinear system of equations has also been updated in line with the new emerging field of hybrid numeric-symbolic solutions to systems of nonlinear equations, ermined system of nonlinear equations on curved manifolds. The von Mises–Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter is devoted to probabilistic regression, the special Gauss–Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation.
A great part of the work is presented in four appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra, and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger algorithm, especially the C. F. Gauss combinatorial algorithm.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Geowissenschaften Geologie Geodäsie, Kartographie, Fernerkundung
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
- Geowissenschaften Geographie | Raumplanung Geodäsie, Kartographie, GIS, Fernerkundung
Weitere Infos & Material
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.