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001450236 001__ 1450236
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001450236 020__ $$a9783030945985$$q(electronic bk.)
001450236 020__ $$a3030945987$$q(electronic bk.)
001450236 020__ $$z9783030945978
001450236 020__ $$z3030945979
001450236 0247_ $$a10.1007/978-3-030-94598-5$$2doi
001450236 035__ $$aSP(OCoLC)1347279694
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001450236 049__ $$aISEA
001450236 050_4 $$aQA278.2
001450236 08204 $$a550.015118$$223
001450236 1001_ $$aAwange, Joseph L.,$$d1969-$$eauthor.$$1https://isni.org/isni/0000000110448480
001450236 24510 $$aApplications of linear and nonlinear models :$$bfixed effects, random effects, and total least squares.
001450236 250__ $$aSecond edition /$$bJoseph Awange, Erik Grafarend, Silvelyn Zwanzig.
001450236 264_1 $$aCham :$$bSpringer,$$c2022.
001450236 300__ $$a1 online resource :$$billustrations (black and white).
001450236 336__ $$atext$$btxt$$2rdacontent
001450236 337__ $$acomputer$$bc$$2rdamedia
001450236 338__ $$aonline resource$$bcr$$2rdacarrier
001450236 4901_ $$aSpringer geophysics
001450236 500__ $$aPrevious edition: published as by Erik W. Grafarend, Joseph L. Awange. 2012.
001450236 504__ $$aIncludes bibliographical references and index.
001450236 5050_ $$aThe First Problem of Algebraic Regression -- The First problem of probabilistic regression - the bias problem -- The second problem of algebraic regression - inconsistent system of linear observational equations -- The second problem of probabilistic regression- special Gauss-Markov model without datum defect - Setup of BLUUE for the moments of first order and of BIQUUE for the central moment of second order -- The third problem of probabilistic regression - special Gauss - Markov model with datum problem -Setup of BLUMBE and BLE for the moments of first order and of BIQUUE and BIQE for the central moment of second order.
001450236 506__ $$aAccess limited to authorized users.
001450236 520__ $$aThis 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 GaussMarkov 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 GrassmannPlucker coordinates, criterion matrices of type TaylorKarman 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 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 on algebraic 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 MisesFisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter is devoted to probabilistic regression, the special GaussMarkov 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.
001450236 588__ $$aDescription based on print version record.
001450236 650_0 $$aGeophysics$$xMathematical models.
001450236 650_0 $$aRegression analysis.
001450236 650_0 $$aLinear models (Statistics)
001450236 655_0 $$aElectronic books.
001450236 7001_ $$aGrafarend, Erik W.,$$eauthor.$$1https://isni.org/isni/0000000109123187
001450236 7001_ $$aZwanzig, Silvelyn,$$eauthor.$$1https://isni.org/isni/0000000360635211
001450236 7001_ $$aGrafarend, Erik W.$$tApplications of linear and nonlinear models.$$sFirst edition.
001450236 77608 $$iPrint version:$$aAwange, Joseph L., 1969-$$tApplications of linear and nonlinear models.$$bSecond edition.$$dCham : Springer, 2022$$z9783030945978$$w(OCoLC)1308494212
001450236 830_0 $$aSpringer geophysics.
001450236 852__ $$bebk
001450236 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-94598-5$$zOnline Access$$91397441.1
001450236 909CO $$ooai:library.usi.edu:1450236$$pGLOBAL_SET
001450236 980__ $$aBIB
001450236 980__ $$aEBOOK
001450236 982__ $$aEbook
001450236 983__ $$aOnline
001450236 994__ $$a92$$bISE