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Bayesian Probability Theory
Applications in the Physical Sciences

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  • format: Hardback
  • isbn: 9781107035904

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  • 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.

    • Uses many real-world applications to show how to perform the numerical evaluations
    • Contains numerical techniques required to solve demanding probabilistic problems numerically
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    Product details

    • format: Hardback
    • isbn: 9781107035904
    • length: 649 pages
    • dimensions: 263 x 180 x 38 mm
    • weight: 1.3kg
    • contains: 128 b/w illus.
  • Table of Contents

    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.

  • Authors

    Wolfgang von der Linden, Technische Universität Graz, Austria
    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.

    Volker Dose, Max-Planck-Institut für Plasmaphysik, Garching, Germany
    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.

    Udo von Toussaint, Max-Planck-Institut für Plasmaphysik, Garching, Germany
    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.

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