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Probability and Statistics in Experimental Physics 1st edition by Byron P Roe ISBN 0387978496 978-0387978499

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Probability and Statistics in Experimental Physics Byron P. Roe Digital Instant Download

Author(s): Byron P. Roe
ISBN(s): 9781475721867, 1475721889
Edition: Corrected
File Details: PDF, 14.09 MB
Language: english
SKU: EB-51449944 Category: Tag:

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Product details: 

ISBN 10: 0387978496

ISBN 13: 978-0387978499

Author:  Byron P. Roe

This book is a practical introduction to the use of probability and statistics in experimental physics for graduate students and advanced undergraduates. It is intended as a practical guide, not as a comprehensive text in probability and statistics. The emphasis is on applications and understanding, on theorems and techniques that are actually used in experimental physics. Proofs of theorems are generally omitted unless they contribute to the intuition in understanding and applying the theorem. The problems, some with worked solutions, introduce the student to the use of computers; occasional reference is made to some of the Fortran routines available in the CERN library, but other systems, such as Maple, will also be useful. Topics covered include: basic concepts and definitions; general results, independent of specific distributions; discrete distributions; the normal distribution and other continuous distributions; generating and characteristic functions; the Monte Carlo method and computer simulations; multi-dimensional distributions; the central limit theorem; inverse probability and confidence limits; estimation methods; curve fitting, robustness estimates, and likelihood ratios; interpolating functions and unfolding problems; fitting data with constraints; robust estimation methods.

Table of contents: 

Basic Probability Concepts

Introduction to fundamental probability principles.

Some Initial Definitions

Key statistical definitions and concepts.

Worked Problems

Homework Problems

Some Results Independent of Specific Distributions

General statistical results applicable across distributions.

Multiple Scattering and the Root N Law

Propagation of Errors; Errors When Changing Variables

Some Useful Inequalities

Worked Problems

Homework Problems

Discrete Distributions and Combinatorials

Analysis of discrete probability distributions and combinatorial methods.

Worked Problems

Homework Problems

Specific Discrete Distributions

In-depth study of particular discrete distributions.

Binomial Distribution

Poisson Distribution

Worked Problems

Homework Problems

The Normal (or Gaussian) Distribution and Other Continuous Distributions

Exploration of continuous probability distributions.

The Normal Distribution

The Chi-square Distribution

F Distribution

Student’s Distribution

The Cauchy Distribution (Breit-Wigner Distribution)

Worked Problems

Homework Problems

Generating Functions and Characteristic Functions

Techniques involving generating and characteristic functions.

Introduction

Convolutions and Compound Probability

Generating Functions

Characteristic Functions

Homework Problems

The Monte Carlo Method: Computer Simulation of Experiments

Utilizing Monte Carlo simulations in experimental physics.

Using the Distribution Inverse

Method of Composition

Acceptance Rejection Method

Computer Pseudo-Random Number Generators

Worked Problems

Homework Problems

Two-Dimensional and Multi-Dimensional Distributions

Analysis of multivariate probability distributions.

Introduction

Two-Dimensional Distributions

Multi-Dimensional Distributions

Theorems on Sums of Squares

Homework Problems

The Central Limit Theorem

Understanding the central limit theorem and its applications.

Introduction; Lindeberg Criterion

Failures of the Central Limit Theorem

Khintchine’s Law of the Iterated Logarithm

Worked Problems

Homework Problems

Inverse Probability; Confidence Limits

Bayesian inference and confidence interval estimation.

Bayes’ Theorem

The Problem of A Priori Probability

Confidence Intervals and Their Interpretation

When Is a Signal Significant?

Worked Problems

Homework Problems

Methods for Estimating Parameters: Least Squares and Maximum Likelihood

Parameter estimation techniques in data analysis.

Method of Least Squares (Regression Analysis)

Maximum Likelihood Method

Putting Together Several Probability Estimates

Worked Problems

Homework Problems

Curve Fitting

Approaches to fitting models to experimental data.

The Maximum Likelihood Method for Multiparameter Problems

Regression Analysis with Non-constant Variance

The Regularization Method

Non-linear Parameters

Robustness of Estimates

Worked Problems

Homework Problems

Bartlett S Function; Estimating Likelihood Ratios Needed for an Experiment

Advanced statistical tools for experimental design.

Introduction

The Jackknife

Making the Distribution Function of the Estimate Close to Normal; the Bartlett S Function

Likelihood Ratio

Estimating in Advance the Number of Events Needed for an Experiment

Homework Problems

Interpolating Functions and Unfolding Problems

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