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.…mehr
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.
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.
Inhaltsangabe
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.
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.
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