This book investigates the relationship between empirical reality and theoretical modelling in Earth sciences, focusing on how empirical experiments and theoretical models interact. It explores the connection between statistics and probability theory, emphasizing the importance of these tools in understanding the physical world. The first chapter addresses the frequency-probability antinomy, while the second chapter discusses the sources of randomness in modelling. Chapters 3 and 4 delve into statistical inference, covering estimation theory and testing theory. Chapter 5 examines the relationship between discrete-finite models and continuous-infinite dimensional models, particularly random fields, making the concepts accessible to geodesists and geophysicists. Chapter 6 explores modern machine learning and deep learning, highlighting their roots in traditional statistical methods and neural networks. The book concludes with a caution against relying solely on empirical evidence and "black box" algorithms, advocating for the integration of physical laws with empirical models to advance understanding of the physical world.

The book is primarily intended for graduate students and researchers in the field of earth sciences with a basic background in probability theory and statistics.

About the Author

Fernando Sans� is professor emeritus at the Polytechnic University of Milan and a Honorary President of the International Association of Geoscience (IAG). He established the International Geoid Service in 1992 and served as its President until 2011. He is a full member of the Accademia dei Lincei, a fellow of the Royal Astronomical Society (UK), and the president of Geomatics and Research Development (GReD), which he founded in 2012. His research areas include gravity field modelling, boundary value problems, statistics, generalized random fields, and GNSS theory.

Sans� has received numerous accolades, including the Bomford Prize for Geodesy in 1979 and the Feltrinelli Award for Astronomy, Geodesy, Geophysics, and Applications in 1986. He holds honorary doctorates from the University of Copenhagen, the University of Thessaloniki, and the University of Stuttgart. Throughout his career, he has (co)-authored over 500 works.

Alberta Albertella is Associate Professor of Geodesy at Politecnico di Milano. She earned her Ph.D in Geodetic, Surveying, and Photogrammetric Sciences from the Politecnico of Turin, Italy, in 1993. She has conducted extensive research in satellite geodesy, specializing in satellite gradiometry and gravity field determination. She contributed to multiple European and Italian satellite missions,. From 2005 to 2012, she was a research partner in the German project GEOTOP, which focused on ocean circulation using geodetic observations. Her expertise includes statistical and numerical data analysis for physical geodesy, geoid estimation, Bayesian methods, and remote sensing. She has also worked on digital mapping, GIS applications, and contributed to Citizen Science projects.

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