Linden / Dose / Toussaint Bayesian Probability Theory

Applications in the Physical Sciences
Erscheinungsjahr 2014
ISBN: 978-1-139-95034-3
Verlag: Cambridge University Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 0 Seiten

From the basics to the forefront of modern research, this book presents all aspects of probability theory, statistics and data analysis from a Bayesian perspective for physicists and engineers. The book presents the roots, applications and numerical implementation of probability theory, and covers advanced topics such as maximum entropy distributions, stochastic processes, parameter estimation, model selection, hypothesis testing and experimental design. In addition, it explores state-of-the art numerical techniques required to solve demanding real-world problems. The book is ideal for students and researchers in physical sciences and engineering.

Autoren/Hrsg.

Linden, Wolfgang von der

Dose, Volker

Toussaint, Udo von

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

Preface
Part I. Introduction:
1. The meaning of probability
2. Basic definitions
3. Bayesian inference
4. Combinatrics
5. Random walks
6. Limit theorems
7. Continuous distributions
8. The central limit theorem
9. Poisson processes and waiting times
Part II. Assigning Probabilities:
10. Transformation invariance
11. Maximum entropy
12. Qualified maximum entropy
13. Global smoothness
Part III. Parameter Estimation:
14. Bayesian parameter estimation
15. Frequentist parameter estimation
16. The Cramer–Rao inequality
Part IV. Testing Hypotheses:
17. The Bayesian way
18. The frequentist way
19. Sampling distributions
20. Bayesian vs frequentist hypothesis tests
Part V. Real World Applications:
21. Regression
22. Inconsistent data
23. Unrecognized signal contributions
24. Change point problems
25. Function estimation
26. Integral equations
27. Model selection
28. Bayesian experimental design
Part VI. Probabilistic Numerical Techniques:
29. Numerical integration
30. Monte Carlo methods
31. Nested sampling
Appendixes
References
Index.

Über Autor(innen)

Linden, Wolfgang von der
Wolfgang von der Linden is Professor for Theoretical and Computational Physics at the Graz University of Technology. His research area is statistical physics with focus on strongly correlated quantum-many-body physics, based on computational techniques.

Dose, Volker
Volker Dose is a former Director of the surface physics division of the Max Planck Institute for plasma physics. He has contributed to Bayesian methods in physics, astronomy and climate research.

Toussaint, Udo von
Udo von Toussaint is a Senior Scientist in the material research division of the Max Planck Institute for plasma physics, where he works on Bayesian experimental design, data fusion, molecular dynamics and inverse problems in the field of plasma-wall interactions.