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.

The Introduction to Bayesian Statistics (2nd Edition) presents Bayes theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters, in a manner that is simple, intuitive and easy to comprehend. The methods are applied to linear models, in models for a robust estimation, for prediction and filtering and in models for estimating variance components and covariance components. Regularization of inverse problems and pattern recognition are also covered while Bayesian networks serve for reaching decisions in systems with uncertainties. If analytical solutions cannot be derived, numerical algorithms are presented such as the Monte Carlo integration and Markov Chain Monte Carlo methods."

The Introduction to Bayesian Statistics (2nd Edition) presents Bayes theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters, in a manner that is simple, intuitive and easy to comprehend. The methods are applied to linear models, in models for a robust estimation, for prediction and filtering and in models for estimating variance components and covariance components. Regularization of inverse problems and pattern recognition are also covered while Bayesian networks serve for reaching decisions in systems with uncertainties. If analytical solutions cannot be derived, numerical algorithms are presented such as the Monte Carlo integration and Markov Chain Monte Carlo methods.

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.

Das Buch fuhrt auf einfache und verstandliche Weise in die Bayes-Statistik ein. Ausgehend vom Bayes-Theorem werden die Schatzung unbekannter Parameter, die Festlegung von Konfidenzregionen fur die unbekannten Parameter und die Prufung von Hypothesen fur die Parameter abgeleitet. Angewendet werden die Verfahren fur die Parameterschatzung im linearen Modell, fur die Parameterschatzung, die sich robust gegenuber Ausreissern in den Beobachtungen verhalt, fur die Pradiktion und Filterung, die Varianz- und Kovarianzkomponentenschatzung und die Mustererkennung. Fur Entscheidungen in Systemen mit Unsicherheiten dienen Bayes-Netze. Lassen sich notwendige Integrale analytisch nicht losen, werden numerische Verfahren mit Hilfe von Zufallswerten eingesetzt."

Das Buch fuhrt auf einfache und verstandliche Weise in die Bayes-Statistik ein. Ausgehend vom Bayes-Theorem werden die Schatzung unbekannter Parameter, die Festlegung von Konfidenzregionen fur die unbekannten Parameter und die Prufung von Hypothesen fur die Parameter abgeleitet. Angewendet werden die Verfahren fur die Parameterschatzung im linearen Modell, fur die Parameterschatzung, die sich robust gegenuber Ausreissern in den Beobachtungen verhalt, fur die Pradiktion und Filterung, die Varianz- und Kovarianzkomponentenschatzung und die Mustererkennung. Fur Entscheidungen in Systemen mit Unsicherheiten dienen Bayes-Netze. Lassen sich notwendige Integrale analytisch nicht losen, werden numerische Verfahren mit Hilfe von Zufallswerten eingesetzt."