Bayesian Inference with Geodetic Applications PDF Download
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Author: Karl-Rudolf Koch
Publisher: Springer
ISBN:
Category : Science
Languages : en
Pages : 244
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Book Description
This introduction to Bayesian inference places special emphasis on applications. All basic concepts are presented: Bayes' theorem, prior density functions, point estimation, confidence region, hypothesis testing and predictive analysis. In addition, Monte Carlo methods are discussed since the applications mostly rely on the numerical integration of the posterior distribution. Furthermore, Bayesian inference in the linear model, nonlinear model, mixed model and in the model with unknown variance and covariance components is considered. Solutions are supplied for the classification, for the posterior analysis based on distributions of robust maximum likelihood type estimates, and for the reconstruction of digital images.
Author: Karl-Rudolf Koch
Publisher: Springer
ISBN:
Category : Science
Languages : en
Pages : 244
Get Book Here
Book Description
This introduction to Bayesian inference places special emphasis on applications. All basic concepts are presented: Bayes' theorem, prior density functions, point estimation, confidence region, hypothesis testing and predictive analysis. In addition, Monte Carlo methods are discussed since the applications mostly rely on the numerical integration of the posterior distribution. Furthermore, Bayesian inference in the linear model, nonlinear model, mixed model and in the model with unknown variance and covariance components is considered. Solutions are supplied for the classification, for the posterior analysis based on distributions of robust maximum likelihood type estimates, and for the reconstruction of digital images.
Author: Karl-Rudolf Koch
Publisher: Springer
ISBN: 3540466010
Category : Science
Languages : en
Pages : 205
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Book Description
This introduction to Bayesian inference places special emphasis on applications. All basic concepts are presented: Bayes' theorem, prior density functions, point estimation, confidence region, hypothesis testing and predictive analysis. In addition, Monte Carlo methods are discussed since the applications mostly rely on the numerical integration of the posterior distribution. Furthermore, Bayesian inference in the linear model, nonlinear model, mixed model and in the model with unknown variance and covariance components is considered. Solutions are supplied for the classification, for the posterior analysis based on distributions of robust maximum likelihood type estimates, and for the reconstruction of digital images.
Author: John D. Bossler
Publisher:
ISBN:
Category : Bayesian statistical decision theory
Languages : en
Pages : 79
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Book Description
Author: John David Bossler
Publisher:
ISBN:
Category : Bayesian statistical decision theory
Languages : en
Pages : 158
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Book Description
Author: Rosario O. Cardenas
Publisher:
ISBN: 9781536132120
Category : MATHEMATICS
Languages : en
Pages : 0
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Book Description
Bayesian Inference: Observations and Applications discusses standard Bayesian inference, in which a-priori distributions are standard probability distributions. In some cases, however, a more general form of a-priori distributions (fuzzy a-priori densities) is suitable to model a-priori information. The combination of fuzziness and stochastic uncertainty calls for a generalization of Bayesian inference, i.e. fuzzy Bayesian inference. The authors explain how Bayes theorem may be generalized to handle this situation. Next, they present a decision analytic framework for completing selection of optimal parameters for machining process definition. In addition, a discussion section on the subjects of inference, experimental design, and risk aversion is included. The concluding review focuses on the sparse Bayesian methods from their model specifications, interference algorithms, and applications in sensor array signal processing. Sparse and structured sparse Bayesian methods formulate problems in a probabilistic manner by constructing a hierarchical model, allowing for the obtainment of flexible modeling capability and statistical information. (Bayesian Inference: Observations and Applications discusses standard Bayesian inference, in which a-priori distributions are standard probability distributions. In some cases, however, a more general form of a-priori distributions (fuzzy a-priori densities) is suitable to model a-priori information. The combination of fuzziness and stochastic uncertainty calls for a generalization of Bayesian inference, i.e. fuzzy Bayesian inference. The authors explain how Bayes theorem may be generalized to handle this situation. Next, they present a decision analytic framework for completing selection of optimal parameters for machining process definition. In addition, a discussion section on the subjects of inference, experimental design, and risk aversion is included. The concluding review focuses on the sparse Bayesian methods from their model specifications, interference algorithms, and applications in sensor array signal processing. Sparse and structured sparse Bayesian methods formulate problems in a probabilistic manner by constructing a hierarchical model, allowing for the obtainment of flexible modeling capability and statistical information.
Author: William A Link
Publisher: Academic Press
ISBN: 0080889808
Category : Science
Languages : en
Pages : 355
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Book Description
This text is written to provide a mathematically sound but accessible and engaging introduction to Bayesian inference specifically for environmental scientists, ecologists and wildlife biologists. It emphasizes the power and usefulness of Bayesian methods in an ecological context. The advent of fast personal computers and easily available software has simplified the use of Bayesian and hierarchical models . One obstacle remains for ecologists and wildlife biologists, namely the near absence of Bayesian texts written specifically for them. The book includes many relevant examples, is supported by software and examples on a companion website and will become an essential grounding in this approach for students and research ecologists. Engagingly written text specifically designed to demystify a complex subject Examples drawn from ecology and wildlife research An essential grounding for graduate and research ecologists in the increasingly prevalent Bayesian approach to inference Companion website with analytical software and examples Leading authors with world-class reputations in ecology and biostatistics
Author: Rosina Ojeda Cárdenas
Publisher:
ISBN: 9781536132137
Category : MATHEMATICS
Languages : en
Pages : 158
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Book Description
Author: Erik W. Grafarend
Publisher: Springer Nature
ISBN: 3030945987
Category : Science
Languages : en
Pages : 1127
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Book Description
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 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 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.
Author: Javier Prieto Tejedor
Publisher: BoD – Books on Demand
ISBN: 9535135775
Category : Mathematics
Languages : en
Pages : 379
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Book Description
The range of Bayesian inference algorithms and their different applications has been greatly expanded since the first implementation of a Kalman filter by Stanley F. Schmidt for the Apollo program. Extended Kalman filters or particle filters are just some examples of these algorithms that have been extensively applied to logistics, medical services, search and rescue operations, or automotive safety, among others. This book takes a look at both theoretical foundations of Bayesian inference and practical implementations in different fields. It is intended as an introductory guide for the application of Bayesian inference in the fields of life sciences, engineering, and economics, as well as a source document of fundamentals for intermediate Bayesian readers.
Author: Jiadong Sun
Publisher: Springer
ISBN: 9811377510
Category : Technology & Engineering
Languages : en
Pages : 612
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Book Description
China Satellite Navigation Conference (CSNC) 2019 Proceedings presents selected research papers from CSNC2019 held during 22nd-25th May in Beijing, China. These papers discuss the technologies and applications of the Global Navigation Satellite System (GNSS), and the latest progress made in the China BeiDou System (BDS) especially. They are divided into 12 topics to match the corresponding sessions in CSNC2019, which broadly covered key topics in GNSS. Readers can learn about the BDS and keep abreast of the latest advances in GNSS techniques and applications.
