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.

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.

Geodesy as the science which determines the figure of the earth, its orientation in space and its gravity field as well as its temporal changes, produces key elements in describing the kinematics and the dynamics of the deformable body "earth". It contributes in particular to geodynamics and opens the door to decode the complex interactions between components of "the system earth". In the breathtaking development recently a whole arsenal of new terrestrial, airborne as well as satelliteborne measurement techniques for earth sciences have been made available and have broadened the spectrum of measurable earth parameters with an unforeseen accuracy and precision, in particular to resolve the factor time. The book focusses on these topics and gives a state of the art of modern geodesy.

This volume gathers the proceedings of the IX Hotine-Marussi Symposium on Mathematical Geodesy, which was held from 18 to 22 June 2018 at the Faculty of Civil and Industrial Engineering, Sapienza University of Rome, Italy. Since 2006, the Hotine-Marussi Symposia series has been produced under the auspices of the Inter-Commission Committee on Theory (ICCT) within the International Association of Geodesy (IAG). The ICCT has organized the last four Hotine-Marussi Symposia, held in Wuhan (2006) and Rome (2009, 2013 and 2018). The overall goal of the ICCT and Hotine-Marussi Symposia has always been to advance geodetic theory, as reflected in the 25 peer-reviewed research articles presented here. The IX Hotine-Marussi Symposium was divided into 10 topical sessions covering all aspects of geodetic theory including reference frames, gravity field modelling, adjustment theory, atmosphere, time series analysis and advanced numerical methods. In total 118 participants attended the Symposium and delivered 82 oral and 37 poster presentations. During a special session at the Accademia Nazionale deiLincei, the oldest scientific academy in the world, six invited speakers discussed interactions of geodesy with oceanography, glaciology, atmospheric research, mathematics, Earth science and seismology.

This book provides an essential appraisal of the recent advances in technologies, mathematical models and computational software used by those working with geodetic data. It explains the latest methods in processing and analyzing geodetic time series data from various space missions (i.e. GNSS, GRACE) and other technologies (i.e. tide gauges), using the most recent mathematical models. The book provides practical examples of how to apply these models to estimate seal level rise as well as rapid and evolving land motion changes due to gravity (ice sheet loss) and earthquakes respectively. It also provides a necessary overview of geodetic software and where to obtain them.

Geodesy: The Concepts, Second Edition focuses on the processes, approaches, and methodologies employed in geodesy, including gravity field and motions of the earth and geodetic methodology. The book first underscores the history of geodesy, mathematics and geodesy, and geodesy and other disciplines. Discussions focus on algebra, geometry, statistics, symbolic relation between geodesy and other sciences, applications of geodesy, and the historical beginnings of geodesy. The text then ponders on the structure of geodesy, as well as functions of geodesy and geodetic theory and practice. The publication examines the motions, gravity field, deformations in time, and size and shape of earth. Topics include tidal phenomena, tectonic deformations, actual shape of the earth, gravity anomaly and potential, and observed polar motion and spin velocity variations. The elements of geodetic methodology, classes of mathematical models, and formulation and solving of problems are also mentioned. The text is a dependable source of data for readers interested in the concepts involved in geodesy.

Geodesy is the science dealing with the determination of the position of points in space, the shape and gravity field of the Earth and with their time variations. This book collects 36 selected papers from the International Symposium on Geodetic Deformation Monitoring held in Jaén (Spain) from 17th to 19th March 2005. It contains a good overview of theoretical matters, models and results.

These proceedings include the written version of 130 papers presented at the International Association of Geodesy IAG2009 "Geodesy for Planet Earth" Scientific Assembly. It was held 31 August to 4 September 2009 in Buenos Aires, Argentina. The theme "Geodesy for Planet Earth" was selected to follow the International Year of Planet Earth 2007-2009 goals of utilizing the knowledge of the world’s geoscientists to improve society for current and future generations. The International Year started in January 2007 and ran thru 2009 which coincided with the IAG2009 Scientific Assembly, one of the largest and most significant meetings of the Geodesy community held every 4 years. The IAG2009 Scientific Assembly was organized into eight Sessions. Four of the Sessions of IAG2009 were based on the IAG Structure (i.e. one per Commission) and covered Reference Frames, Gravity Field, Earth Rotation and Geodynamics, and Positioning and Applications. Since IAG2009 was taking place in the great Argentine city of Buenos Aires, a Session was devoted to the Geodesy of Latin America. A Session dedicated to the IAG’s Global Geodetic Observing System (GGOS), the primary observing system focused on the multidisciplinary research being done in Geodesy that contributes to important societal issues such as monitoring global climate change and the environment. A Session on the IAG Services was also part of the Assembly detailing the important role they play in providing geodetic data, products, and analysis to the scientific community. A final Session devoted to the organizations ION, FIG, and ISPRS and their significant work in navigation and earth observation that complements the IAG.