Probability and Statistics in Experimental Physics

1. Front Matter

   Pages i-x

   PDF

2. Basic Probability Concepts

   • Byron P. Roe

   Pages 1-4

3. Some Initial Definitions

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   Pages 5-13

4. Some Results Independent of Specific Distributions

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   Pages 14-26

5. Discrete Distributions and Combinatorials

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   Pages 27-32

6. Specific Discrete Distributions

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   Pages 33-41

7. The Normal (or Gaussian) Distribution and Other Continuous Distributions

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   Pages 42-53

8. Generating Functions and Characteristic Functions

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   Pages 54-61

9. The Monte Carlo Method: Computer Simulation of Experiments

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   Pages 62-74

10. Two Dimensional and Multi-Dimensional Distributions

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    Pages 75-89

11. The Central Limit Theorem

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    Pages 90-101

12. Inverse Probability; Confidence Limits

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    Pages 102-117

13. Methods for Estimating Parameters. Least Squares and Maximum Likelihood

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    Pages 118-134

14. Curve Fitting

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    Pages 135-160

15. Bartlett S Function; Estimating Likelihood Ratios Needed for an Experiment

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    Pages 161-172

16. Interpolating Functions and Unfolding Problems

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    Pages 173-179

17. Fitting Data with Correlations and Constraints

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    Pages 180-188

18. Beyond Maximum Likelihood and Least Squares; Robust Methods

    • Byron P. Roe

    Pages 189-200

19. Back Matter

    Pages 201-208

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This book is meant to be a practical introduction into the use of probability and statistics in experimental physics for advanced undergraduate students and for graduate students. I have attempted to write a short book. It is not intended as a comprehensive text in probability and statistics. I have tried to emphasize areas I have found to be useful when doing experimental physics. Except for the first two chapters the emphasis is on applications and understanding. I have omitted proofs of formal theorems in the interests of brevity unless I felt the proof added to one's intuition in understanding and applying the theorem. Since, however, this is a field in which there are often a number of misunderstandings, it is necessary to state some things with reasonable precision. I have tried to do this when necessary. I assume the student is familiar with partial derivatives and with ele­ mentary matrix manipulation. A computer is a needed tool for probability and statistics in experimental physics. We will introduce its use in this subject in some of the homework problems. One may interact with a computer in a batch mode or an inter­ active mode. In a batch mode, one submits FORTRAN or other language programs, the computer processes them, and returns the end results. In the interactive mode, one gives the computer an instruction, the computer processes it, indicates what it has done, and waits for the next instruction.

• Monte Carlo method
• Parameter
• experiment
• experimental physics
• normal distribution
• statistics

• Randall Laboratory of Physics, Ann Arbor, USA

  Byron P. Roe

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