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Introduction to Bayesian Statistics
This book presents Bayes’ theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters. It does so in a simple manner that is easy to comprehend. The book compares traditional and Bayesian methods with the rules of probability presented in a logical way allowing an intuitive understanding of random variables and their probability distributions to be formed.
Parameter Estimation and Hypothesis Testing in Linear Models
A treatment of estimating unknown parameters, testing hypotheses and estimating confidence intervals in linear models. Readers will find here presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model as well as the mixed model for estimating random parameters. A chapter on the robust estimation of parameters and several examples have been added to this second edition. The necessary theorems of vector and matrix algebra and the probability distributions of test statistics are derived so as to make this book self-contained. Geodesy students as well as those in the natural sciences and engineering will find the emphasis on the geodetic application of statistical models extremely useful.
Bayesian Inference with Geodetic Applications
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.
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The Use of Artificial Satellites for Geodesy
Published by the American Geophysical Union as part of the Geophysical Monograph Series, Volume 15. This monograph contains 34 communications presented at the Third International Symposium on the Use of Artificial Satellites for Geodesy in 1971, and 4 invited papers on subjects that complement the others and provide continuity. All contributions represent the most recent findings in the theoretical and applied fields of satellite geodesy, including new instrumentation (satellite sensors and ground equipment) of potential use in satellite geodesy. The two preceding symposiums were held at Washington, D.C., in 1962 and at Athens, Greece, in 1965. The Proceedings of the first were published by North-Holland Publishing Company, Amsterdam, in 1963, and the Proceedings of the second by the National Technical University, Athens, in 1967. The prime mover behind both was George Veis, and his continuing dedication to this subject was in large measure responsible for scheduling this third symposium.
